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Jyothi

                    UNITS, DIMENSIONS AND MOTION



                 objective questions

1)At the initial instant, a body is at a point (- 2, 4). The body is then moved to the point (2, 1). Then the displacement of the body is:

a. 4 m b. 3 m c. 5 m d. 0 e. 9 m

2)A person initially moves through a distance 5 km towards south and then 12 km due east. His displacement is:

a. 17 km b. 7 km c. 8.5 km d. 13 km e. none of these

3)A car, moving at a speed 30 km/h, covers half the distance to the destination in a certain time. At what speed should it move further to be able to reach the destination and then back to the starting point during the same span of time?

a. 30 km/h b. 60 km/h c. 45 km/h d. 120 km/h e. 90 km/h

4)A traveler caught in a thunderstorm saw the flash of lightning and heard the thunder 10 s later. The distance at which lightning took place is (speed of sound = 340 m/s):

a. 34 km b. 3.4 km c. 0.34 km d. 340 km e. 0.034 km

5)Two cars move along mutually perpendicular roads towards a crossing. At a certain instant the first car has a speed 27 km/h and is at a distance 300 m from the crossroads. At that instant the other car is at a distance 450 m from the crossroads. What must be the speed of the second car so that it reaches the crossing 5 seconds after the first car has passed it?

a. 36 km/h b. 27 km/h c. 30 km/h d. 54 km/h e. 40.5 km/h

6)A motorcar moves westwards with a velocity 80 km/h. another car moves at the same velocity towards the first car. At an instant the distance between them is 10 km. The time after which they meet is:

a. 3.75 min b. 0.375 min c. 37.5 min d. 3.75 h e. 0.375 h

7)While traveling from one location to another, a motorcar has a constant velocity 60 km/h over half the time. What is its constant velocity during the remaining time of travel if its average velocity during the motion is 65 km/h?

a. 62.5 km/h b. 50.25 km/h c. 73 km/h d. 70.9 km/h e. none of these

8)The period of a body under S. H. M is represented by the equation T = P^{a Db Sc, where P is pressure, D is the density and S is surface tension. Then the value of a, b and c are respectively:}

a. ? 1, - 2, 3 b. 1, 2, 1/3 c. ½, - 3/2, - 1/2 d. ? 3/2, ½, 1 e. 2, -1, - 3

9)A physical quantity is represented by the equation A = Ma Lb Tc. If the percentage error in the measurements of M, L and T are respectively x, y and z, then the total percentage error in A is:

a. ax + by + cz b. ax ? by ? cz c. ay ? bx + cz d. ax ? by ? cz e. none

10)A pressure of 106 dyne.cm² is equivalent to:

a. 106 N/m² b. 108 N/m² c. 105 N/m² d. 1010 N/m² e. 107 N/m²

11)A person standing on the top of a tower of height 50 m throws a ball vertically upwards with a velocity 20 m/s. How high the ball will rise above the tower?

a. 20 m b. 30 m c. 40 m d. 10 m e. 70 m

12)A helicopter is rising steadily at a speed 7 m/s. While it is at a height of 196 m above the ground, a packet is dropped from it. The velocity with which it hits the ground is:

a. 62.5 m/s b. 19.6 m/s c. 48.6 m/s d. 196 m/s e. none of these

13)An airplane is flying at an altitude 2 km at a speed 500 km/h. How much away from a target must a bomb be dropped from the plane so that it hits the target?

a. 500 m b. 1000 m c. 1777.7 m d. 2777.7 m e. 3777.7 m

14)The second?s hand of a clock is 2 cm long. Then the speed of the tip of the hand is:

a. 2.1 cm/s b. 21 cm/s c. 0.021 cm/s d. 0.21 cm/s e. 1 cm/s

15)A body, thrown upwards with a velocity 9.8 m/s from the top of a tower reaches the ground after 4 s. Height of the tower is:

a. 100 m b. 80 m c. 60 m d. 40 m e. 20 m

16)A motorcyclist covers half the distance at a speed 40km/h, the next one-fourth of the distance with a speed 30 km/h and the rest of the distance with a speed 60 km/h. His average speed during the whole journey is:

a. 80 km/h b. 50 km/h c. 40 km/h d. 130/3 km/h e. 117/3 km/h

17)A car decelerates to rest uniformly from 20 m/s, in 4 s and then reverses with uniform acceleration back to the starting point, also in 4 s. The average velocity of the car during the travel is:

a. 20 m/s b. 10 m/s c. 0 m/s d. 40 m/s e. none of these

18)The dimensional formula for Planck?s constant is:

a. MLT b. M L² T ? 1 c. M L T ? 1 d. M L² T ? 2 e. M² L² T ? 1

19)The displacement of a particle ?x? is related to time ?t? as t = ? x² + ? x, where ? and ? are constants. Then the retardation of the particle is (v is velocity):

a. 2 ? v³ b. 2 ? v³ c. 2 ? ? v² d. 2 ?² v³ e. 2 ?² v³

20)When a body is moving with constant speed along a circular path:

a. its velocity remains constant b. no force acts on the body c. no work is done on the body d. no acceleration is experienced by the body e. all the above are correct

21)Planck?s constant has the dimensions of:

a. energy b. momentum c. force d. frequency e. angular momentum

22)The dimensional formula [ML²T ? 3] represents:

a. force b. momentum c. energy d. angular velocity e. power

23)Unit of pressure in S. I. system is:

a. dyne/cm² b. m of mercury c. mm of mercury d. pascal

e. none of these

24)The angular velocity of the minutes needle of the wall clock (in rad/minute) is:

a. ? b. ?/60 c. ?/30 d. 2? e. ?/2

25)A body of mass m is moving in a circular path of radius ?r? with a constant speed ?v?. The work done by the centripetal force as the body covers one-fourth the distance along the circle is:

a. mvr b. mv²r c. zero d. ?mv²/2 e. ?2 mv²

26)A boy standing near the edge of a cliff throws two balls, one vertically upwards and the other vertically downwards with the same velocity ?v?. The ratio between their velocities on reaching the foot of the cliff is:

a. 1:2 b. 2:1 c. 1:3 d. 3:1 e.1:1

27)A motorcyclist covers half his journey with a speed 40 km/h, the next one-third at a speed 30 km/h and the rest at 60 km/h. The average speed of the man during the whole journey is:

a. 130/3 km/h b. 80 km/h c. 50 km/h d. 40 km/h e. 47.5 km/h

28)A ball is dropped from a height inside an elevator, which is accelerating upwards at the rate ?a?. The acceleration of the ball is:

a. g + a upward b. g ? a upward c. g ? a downward d. a upward

e. g downward

29)A person is walking on a straight road and has a velocity v for t seconds and V for the next t seconds. His average velocity over the time interval 2t is:

a. (v + V)/2 b. v V/(v + V) c. 2 v V/(v + V) d. v V/2(v + V) e. ?(v V)

30)Two bullets are fired simultaneously in the horizontal direction from the top of a building, with different speeds. Which one will hit the ground first?

a. the faster one b. the slower one c. depends on their mass also d. both will hit at the same instant e. none of the above

31)The range of a projectile fired with a certain velocity, making an angle 15º with the horizontal, is 50 m. If it is fired at an angle 45º with the horizontal and with the same velocity, the range will be:

a. 50 m b. 100 m c. 37 m d. 25 m e. 75 m

32)An object having an initial velocity 4 m/s is accelerated at a steady rate of 1.2 m/s² for 5 seconds. The distance moved by it during the period of acceleration is:

a. 5 m b. 15 m c. 25 m d. 35 m e. 45 m

33)A bullet having muscle velocity 16 m/s penetrates a block of wood and comes to rest inside it in 0.4 s. The time for which it has been retarding is:

a. 0.05 s b. 0.5 s c. 5 s d. 0.25 s e. 0.025 s

34)A car moving at a speed 60 km/h overtakes another one moving at 42 km/h. If each car is 5 m long, the time taken for overtaking is:

a. 1 s b. 2 s c. 3 s d. 4 s e. 5 s

35)A staircase has three steps each 10 cm high and 20 cm wide. The minimum velocity with which a ball must roll off the topmost step so that it may directly hit the lowest plane is:

a. 1 m/s b. 2 m/s c. 3 m/s d. 5 m/s e. 0.5 m/s

36)Three particles A, B and C are situated at the vertices of an equilateral triangle of side ?a? at the instant t = 0. They now start moving with the same speed ?v? each such that at every instant A is moving towards B, B towards C and C towards A. Then after how much time will they all meet?

a. a/v b. 2a/v c. a/3v d. 3a/2v e. 2a/3v

37)A body is projected with a certain velocity in a direction making a certain angle with the horizontal. Then which of the following statements is true?

a. its velocity remains the same throughout the motion

b. its acceleration remains the same throughout the motion

c. its direction of motion is the same throughout

d. all the above

e. none of the above

38)The average velocity of a projectile, projected with a velocity 30 m/s at an angle 60º with the horizontal, between the instants when it passes half the maximum height is:

a. 30 m/s b. 15 m/s c. 10 m/s d. 20 m/s e. 0

39)An elevator is descending at a uniform acceleration. A coin dropped from a height 6 m inside the elevator is found to hit the floor of it in 1 second. Then the acceleration of the elevator is:

a. b. c. d. e.

40)A bomb is dropped from an airplane flying horizontally with a constant velocity. Assuming that the bomb explodes on its way downward, the point at which it explodes will be:

a. in front of the plane, and below it b. behind the plane and below it c. above the plane in front d. behind the plane and above it e. vertically below the plane

41)An airplane is heading from a point A to another point B, situated at a distance 500 m in a direction 30º east of north. Wind is blowing due north at speed 20 m/s and the speed of the plane is 150 m/s. Then the direction in which the pilot should head the plane is:

a. Sin ? 1 (1/15) east of the line AB b. Cos ? 1 (1/15) east of the line AB

c. Sin ? 1 (1/15) west of the line AB d. Cos ? 1 (1/15) west of the line AB e. none of these

42)A particle moves along the X-axis in accordance with the equation: x = u (t ? 2) + a (t ? 2)², t is in seconds. Then:

a. The initial velocity of the particle is u b. the acceleration of the particle is a

c. acceleration of the particle is 4a d. at t = 2 s, the particle is at the origin e. none of the above is correct

43)Find out the correct statement from the following:

a. magnitude of velocity of a particle is its speed b. the magnitude of the average velocity over an interval of time is the same as its average speed in that interval c. it is possible that the average velocity is zero but the average speed is non-zero d. it is possible that the average speed is zero but average velocity is non-zero e. none of the above are correct

44)The distance of a planet from the earth is 3.66 × 10 8 m. The angular diameter of the planet is 1.5º. Then the diameter of the planet is:

a. 9.6 × 10 6 m b. 9.6 × 10 7 m c. 9.6 × 10 8 m d.9.6 × 10 5 m e. 9.6 × 10 4 m

45)A radio signal sent from a RADAR to an airplane returns to the radar after 12 ? s. The distance of the plane is:

a. 1.8 km b. 4.8 km c. 48 km d. 18 km e. 180 km

46)The suitable unit for measuring the radius of a nucleus is:

a. A. U b. Å c. micron d. meter e. fermi

47)Barn is unit of:

a. length b. volume c. area d. angle e. temperature

48)In the equation y = A Sin (?t ? kx), the dimensional formula for ? is:

a. [M 0 L ? 1 T 0] b. [M ?1 L ? 1 T 0 ] c. [M 0 L 0 T ?1 ] d. [M 0 L 0 T 0 ] e. none of these

49)The dimensional formula for light year is:

a. L b. T c. LT ?1 d. LT ?2 e. T²

50)Velocity acquired by a body moving with uniform acceleration is 40 m/s in 2 s and 60 m/s in 4 s. Then the initial velocity of the body is:

a. 0 b. 5 m/s c. 10 m/s d. 15 m/s e. 20 m/s

51)A body covers 1/3rd distance with velocity 10 m/s, the second 1/3rd distance with velocity 20 m/s and the remaining distance with velocity 30 m/s. The average velocity of the body during the whole journey is:

a. 8.4 m/s b. 12.4 m/s c. 16.4 m/s d. 20.4 m/s e. 24.4 m/s

52)A body covers a distance 10 m along a semicircular path. The ration of its distance traveled to the displacement is:

a. 22:7 b. 11:7 c. 12:5 d. 8:3 e. 7:5

53)A body moves along the sides AB, BC and CD of a square of side 25 m with a velocity 15 m/s each. The average velocity of the body is:

a. 5 m/s b. 10 m/s c. 15 m/s d. 20 m/s e. 7.5 m/s

54)For a body starting from rest, the time during which it covers a certain displacement with uniform acceleration is:

a. directly proportional to square root of displacement b. directly proportional to displacement c. inversely proportional to square root of displacement d. inversely proportional to displacement e. directly proportional to the cube of displacement

55)The equation of motion of a body is s = 6 t² - 4 t³. Its motion is:

a. uniform b. uniformly accelerated c. uniformly retarded

d. non-uniformly accelerated e. non-uniformly retarded

56)The angle between the vectors 2i ? j + 2k and 4i + 3j is:

a. Cos ? 1(2/3) b. Cos ? 1(1/3) c. Cos ? 1(?2/3) d. Cos ? 1?(3/7) e. Cos ? 1(?3/2)

57)The rectangular components of a force 13 N are:

a. 5 N & 12 N b. 6.5 N & 6.5 N c. 12 N & 9 N d. 10 N & 11N e. none of these

58)A force 4i + j ? 2k newton acting on a body imparts a velocity 2i + 2j + 3k to it. Then the power developed is:

a. 2 W b. 4 W c. 5 W d. 10 W e. 8 w

59)To get a resultant displacement of 10 m, two displacement vectors of magnitudes 6 m and 8 m have to be combined:

a. parallel to each other b. anti-parallel to each other c. at an angle 60º

d. at an angle 120º e. at right angles

60)A ball is dropped out from a moving train. The motion of the ball as seen by the man inside the train is along:

a. a vertical straight line b. a parabolic. an ellipse d. a horizontal straight line e. a hyperbola

solutions

1. If we write the position vectors of the two positions, we get, the initial position vector = - 2i + 4j and the final position vector = 2i + j. Then the displacement in vector form is ? 4i + units

Correct choice: c

The two directions of motion are mutually perpendicular. Hence the displacement is the vector sum of the two = 13 km (see the figure below)

5 km 13 km

12 km

Correct choice: d

3. Let the time taken to cover half the distance (s) be ?t?. Then the remaining 1 ½ times the distance is covered in the same time. And t = (s/2)/30 = s/60 h. Taking an equal amount of time the body should travel the rest of the distance = 3s/2. Hence the speed = distance / time = (3s/2)/(s/60) = 90 km/h

Correct choice: e

4. Here the required distance is the distance traveled by sound = velocity of sound × time = 340 × 10 = 3400 m = 3.4 km.

Correct choice: b

5. Speed of the first car = 27 km/h = 27 × 5/18 = 15/2 m/s.

Time taken by it to reach the junction = distance/speed = 300/(15/2) = 40 s.

The other car must reach the junction taking 40 + 5 = 45 s, covering a distance 450 m.

Hence its speed = 450/45 = 10 m/s = 10 × (18/5) = 36 km/h.

Correct choice: a

6. The two cars are moving in opposite directions. Hence their relative velocity = 160 km/h. Now assuming one of the cars to be stationary and the other approaching with a speed 160 km/h, the time taken to travel the distance of 10 km, in order that they meet = 10/160 h = (1/16) × 60 = 3.75 minutes.

Correct choice: a

7. Half the distance is covered with a velocity 60 km/h. If s is the total distance, time to cover half the distance = (s/2)/60 = s/120 hour. The remaining half the distance let it travel with a velocity v. Then average velocity = total displacement / total time.

Or, 65 = s/[s/120 + s/2v]. Solving this equation, we get v = 70.9 km/h

Correct choice: d

8. Use the method of dimensions and evaluate a, b and c.

Dimensions of pressure P = force/area = [ML^{? 1 T ? 2 ].}

Dimensions of density = mass/volume = [M L ? 3 ].

Dimensions of surface tension = force / length = [M T ? 2].

The result is a = - 3/2, b = ½ and c = 1

Correct choice: d

9. Percentage error in this case = ax + by + cz. In case of any doubt refer to the formulae given along with the first set of questions.

Correct choice: a

10. As you know, 1 N = 10 5 dynes and 1 m² = 10 4 cm².

Hence 10 6 dyne/cm² = 106 × 10 ? 5 / 10 ? 4 = 10 5 N/m²

Correct choice: c

11. Here height of the tower is insignificant, because we need only the height above the tower up to which the ball rises. Use the formula, v = u ? 2gh. i.e., here, 0 = 20² - 2 × 10 × h.

Hence h = 400/20 = 20 m.

Correct choice: a

12. When a body is dropped from a rising helicopter, the body will initially have the same upward velocity as the copter. And on returning to the same height from which it is dropped, after rising to the maximum height it will have the same old velocity of 7 m/s, in the present problem. Thus, with an initial downward velocity of 7 m/s it falls through a height 196m. Hence using the formula, v² = u² + 2gh, we get v² = 7² + 2 × 9.8 × 196. Or, v ? 62.5 m/s.

Correct choice: a

13. As the bomb is dropped, it continues to move in the horizontal direction with the velocity of the plane, and at the same time moving vertically downwards. And therefore it follows a parabolic path and hits the ground at a certain distance away from the point from where it has been dropped. The horizontal distance = horizontal velocity ?v? × time taken to reach the ground ?t?

The value of t is got by using the formula, s = ½ gt², i.e., 2000 = ½ × 10 × t².

Hence t² = 400, or t = 20 seconds.

The horizontal distance = v t = 500 km/h × (5/18) × 20 = 2777.7 m.

Correct choice: d

14. Angular velocity of the seconds hand ? = angular displacement / time = 2?/60 = ?/30 rad/s

Hence the linear velocity of its tip = r? = 2 × ?/30 = 0.21 cm/s

Correct choice: d

15. The body is thrown upwards and it effectively moves down and reaches the ground and therefore the formula to be used is: - s = ut ? ½ gt² = 9.8 × 4 ? ½ × 9.8 × 4² = 9.8 × 4 ? 9.8 × 8 = - 4 × 9.8 = - 39.2. Hence s = 39.2 m ? 40 m

Correct choice: d

16. If s is the total distance traveled, then the total time taken = s/(2 × 40) + s/(4 × 30) + s/(4 × 60)

= (3 s + 2 s + s)/240 = 6s/240 = s/40 hour. Hence the average speed = total distance/total time

= s/(s/40) = 40 km/h.

Correct choice: c

17. Since the effective displacement = 0, the average velocity is = 0.

Correct choice: c

18. Energy = Planck?s constant times frequency = Planck?s constant/period.

Hence Planck?s constant has dimensions of energy times period = [ML² T ? 2] [T] = [ML² T ? 1]

Correct choice: b

19. Given t = ? x² + ? x. Differentiating with respect to t, we get, 1 = 2 ? x dx/dt + ? dx/dt

Or, 1 = 2 ? x v + ? v = v[2 ? x + ?]. Differentiating again, 0 = 2 ? [x dv/dt + v dx/dt] + ? d²x/dt²

Or, 0 = 2 ? [x a + v v] + ? a = [2 ? x + ?] a + 2 ? v², where ?a? is acceleration.

Hence, [2 ? x + ?] a = - 2 ? v², or (1/v) a = - 2 ? v², Or, a = - 2 ? v³ (negative sign shows retardation).

Correct choice: b

20. During motion along a circular path, the force on the body is centripetal force, directed towards the center of the path. In other words, motion and force are mutually perpendicular and hence no work is done.

Correct choice: c

21. Angular momentum of electrons in an atom, according to Bohr is nh/2?, where n is a mere number and 2? is dimensionless constant. Hence the dimensions of ?h?, Planck?s constant, are those of angular momentum.

Correct choice: e

22. The given dimensional formula is that of energy/time, or power.

Correct choice: e

23. As you know, the unit of pressure is N/m², which is pascal.

Correct choice: d

24. Minutes needle completes one rotation in 60 minutes and hence its angular velocity = 2?/60 = ?/30 radian/minute.

Correct choice: c

25. See solution no. 20. The answer is zero.

Correct choice: c

26. For the ball thrown vertically up, on reaching the cliff back after moving to the maximum height is the same as the velocity with which it is thrown up. Thus, considering the motion of the two bodies we see that they both have the same initial velocity downwards. Hence they both reach the bottom with the same velocity. Hence the answer is 1:1

Correct choice: e

27. Average speed = total distance s/ total time t

And t = (s/2)/40 + (s/4)/30 + (s/4)/60 = s/80 + s/120 + s/240 = s/40

So, the average speed = s/(s/40) = 40 km/h.

Correct choice: d

28. Once a body is dropped it falls under gravity and hence its acceleration is acceleration of gravity acting vertically downwards.

Correct choice: e

29. Average velocity = total displacement / total time = (vt + Vt)/2t = (v + V)/2.

Correct choice: a

30. Both the bullets are fired from the same point and hence before hitting the ground they travel the same vertical distance. Vertical motion is affected only by gravity and hence their motions are identical and therefore they both reach the ground at the same instant. Note that the slower one will hit at a nearer point and the faster one at a farther point.

Correct choice: d

31. Range of a projectile R = u² sin2? / g. Hence here, 50 = u² sin30 / g = u²/2g, since sin30 = ½.

For angle of projection 45º, range is maximum = u²/g. From the above equation we see that u²/g = 100

Correct choice: b

32. Here use the formula s = ut + ½ at². s = 4 × 5 + ½ 1.2 × 5² = 20 + 15 = 35 m

Correct choice: d

33. Use the formula v² = u² + 2as, then we have, 0 = 16² + 2 × a × 0.4. Or, a = - 16²/0.8 = - 320 m/s²

Now, we have v = u + at, or 0 = 16 + (- 320) t. Hence t = 16/320 = 0.05 s

Correct choice: a

34. In this problem the relative velocity = 60 ? 42 = 18 km/h = 5 m/s.

And for overtaking the distance to be covered is 5 + 5 = 10 m. Hence the time taken = distance/speed

= 10/5 = 2 s.

Correct choice: b

35. In this problem, the ball should move simultaneously 20 cm down and 40 cm horizontally, because in that case, the ball can just clear the edge of the last step.

Time taken to fall through 20 cm = 0.2 m is given by s = ½ gt², or, 0.2 = ½ × 10 × t²

Hence t² = 0.4/10 = 0.04. Hence t ? 0.2 s. Hence to cover a horizontal distance of 0.4 m, the velocity = 0.4/0.2 = 2 m/s.

Correct choice: b

36. All the particles effectively move towards the center of the triangle and meet there. It is equivalent to the balls moving towards the center with a velocity v cos30 = ?3 v/2, over a distance = 2/3 the altitude of the triangle. Altitude = ?[a² - (a/2)²] = ?3 a/2. Hence the distance moved by each particle = (2/3)(?3 a/2) = a/?3. Hence the time taken = (a/?3)/ (?3 v/2) = 2a/3v.

Correct choice: e

37. Any body projected freely will move effectively downwards with the acceleration due to gravity, which is a constant.

Correct choice: b

38. The projectile is at half the height twice during the motion, as the motion is along a parabolic path. Between these two positions, the resultant vertical displacement = 0 and hence the average vertical velocity = 0. But the horizontal velocity remains constant at 30 cos60 = 30 × ½ = 15 m/s

Correct choice: b

39. As the coin falls downwards, under gravity, the lift also moves downwards with an acceleration ?a?. Hence the resultant acceleration of the coin is g ? a. Hence here, 2 = ½ (g - a)t² = ½ (g - a), since t = 1 s. Therefore, g - a = 4 and hence a = g ? 4 = 10 ? 4 = 6 m/s²

Correct choice: b

40. As the bomb is dropped from the plane, it will continue to move in the horizontal direction, along with the plane, and at the same time falling downwards. Hence when looked from the plane it will appear vertically below the plane and its motion is along a vertical straight line. But for a man standing on the ground it will appear to be moving along a parabolic path.

Correct choice: e

41. Look at the vector diagram below. Let ? be the angle between the line AB and the direction of motion of the plane. Applying the law of sines we get 20/sin ? = 150/sin30 = 300.

Hence sin? = 20/300 = 1/15. So ? = sin ? 1(1/15), east of the line AB.

B

20 m/s 30º 150 m/s

A

Correct choice: a

42. The given equation is of the form s = ut + ½ at²

But here in the place of ?t? we have t ? 2 and therefore, at t = 2 s, displacement = 0.

Correct choice: d

43. If a particle starts from a point and reaches back the same point after a journey, the net displacement and hence the average velocity is zero. But the distance traveled is not zero and hence speed is not zero. But if speed is zero, average velocity is also zero, since the particle has not moved at all.

Correct choice: c

44. When the angular diameter ? and distance or the radius ?r? vector are given, the diameter d = r?, where ? must be in radian. Hence d = 3.66 × 10 8 (1.5 × ?/180) = 9.6 × 10 6 m

Correct choice: a

Here the signal travels twice the distance ?d? between the plane and the transmitter.

So, 2d = velocity times time = 3 × 10 8 × 12 × 10 ? 6 = 3600 m. Hence d = 1800 m = 1.8 km

Correct choice: a

Radius of the nucleus is of the order of femto-meter or fermi (10 ? 15 m).

Correct choice: e

Barn is the unit of area

Correct choice: c

The dimensional formula is that of 1/period T

Correct choice: c

Light year is distance

Correct choice: a

In this problem using the formula, v = u +at, we have two equations: 40 = u + 2a and

60 = u + 4a. Solving these two simple linear equations we get u = 20 m/s

Correct choice: e

51. The total time of journey t = (s/3)/10 + (s/3)/20 + (s/3)/30 = s/30 + s/60 + s/90 = (6s + 3s + 2s)/180

= 11s/180. So, the average velocity = s/t = 180/11 = 16.4 m/s

Correct choice: c

52 If ?r? is the radius of the path, then, 10 = ? r, or r = 10/?. Displacement is then 2r

So, distance/displacement = 10 / 2 r = 10 / (20/?) = ?/2 = 22/14 = 11/7

Correct choice: b

53 In this case the effective displacement is the side AD = 25 m and the time taken is 3 × 25/15 = 5

Therefore the average velocity = 25/5 = 5 m/s.

Correct choice: a

54 For a body starting from rest, s = ½ at². So, time of travel is proportional to square root of displacement.

Correct choice: a

55 Here the displacement s = 6t² - 4t³. Hence velocity v = ds/dt = 12t ? 12t² and

Acceleration a = dv/dt = 12 ? 24t. Thus acceleration is negative (except at t = 0) and is dependent on t. Hence the motion is non-uniformly retarded.

Correct choice: e

56 If the vectors are taken as A and B, then we have A . B = ABCos?.

So, cos? = A . B / AB. A.B = 8 ? 3 = 5 and A = 3 and B = 5 (square root of the sum of the squares of the coefficients of i, j and k). Hence cos? = 5/15 = 1/3. Or, ? = cos ? 1(1/3)

Correct choice: b

57 Rectangular components are those, which are mutually perpendicular. S0, 5 and 12 N making 90º with each other results in 13 (square root of the sum of the squares of 5 and 12)

Correct choice: a

58 Power = dot product between force and velocity. So, here power = (4i + j ? 2k) . (2i + 2j + 3k)

= 8 + 2 ? 6 = 4 units

Correct choice: b

59 The displacements 6 m and 8 m at right angles to each other results in 10 m.

Correct choice: e

60 A similar problem was there here earlier. And the answer is vertical straight line.

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