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1. A cubical block of mass m &edge ?a? slides down a rough inclined plane of inclination 0 with a uniform velocity. Find the torque of normal force acting on the block about its centre.

Ans. mga sin0

------------

2

2. What is radial equilibrium?

3. How to know whether cart is moving on an incline(with uniform velocity) or on a horizontal plane (accelerated)?

4. Which is distilled first?

a. liquid H₂b. liquid O₂ c. liquid CO₂ d. liquid N₂

what happens when chlorobenzene is subjected to hydrolysis?

Q) Is magnetic force conservative?

22.03.2008

Physics

1. A cubical block of mass m &edge ?a? slides down a rough inclined plane of inclination 0 with a uniform velocity. Find the torque of normal force acting on the block about its centre.

Ans. mga sin0

------------

2

????????????????????????????????????????????????

2. All surfaces frictionless. What is the velocity of smaller block when it reaches the bottom?

Ans. [2m²ghcos²?]^1/2

---------------------------

[(M+m)(M+msin²?)]^1/2

????????????????????????????????????????????????

3. All surfaces frictionless.

(1)Speed of smaller block when it breaks off at a height h.

(2)Max. height from ground the smaller block will ascend.

(3)Show that the smaller block will land again on the larger mass.

(4)Distance traversed by the bigger block during the time the smaller block was in flight under gravity.

Ans. (1) (M²+Mm+m²) v²

{ -------------------- ? 2gh}^1/2

(M+m)²

(2) Mv²(4) 2mv [Mv²-2(M+m)gh]^1/2

------------ -------------------------------

2g(M+m) g(M+m)^3/2

???????????????????????????????????????????????.

4. A small block of superdense material has a mass M_e/2. It is situated at a height ?h? above the earth?s surface.(h<<R_e).

Find its speed when the height reduces to ?h?/2.

(M_e=6x 10²⁴ kg). Ans.(2gh/3)^1/2

???????????????????????????????????????????????.

5. What is radial equilibrium?

???????????????????????????????????????????????..

6.How to know whether cart is moving on an incline(with uniform velocity) or on a horizontal plane (accelerated)?

????????????????????????????????????????????..

22.03.2008

Physics

1. A cubical block of mass m &edge ?a? slides down a rough inclined plane of inclination 0 with a uniform velocity. Find the torque of normal force acting on the block about its centre.

Ans. mga sin0

------------

2

????????????????????????????????????????????????

3. All surfaces frictionless.

(1)Speed of smaller block when it breaks off at a height h.

(2)Max. height from ground the smaller block will ascend.

(3)Show that the smaller block will land again on the larger mass.

(4)Distance traversed by the bigger block during the time the smaller block was in flight under gravity.

Ans. (1) (M²+Mm+m²) v²

{ -------------------- ? 2gh}^1/2

(M+m)²

(2) Mv²(4) 2mv [Mv²-2(M+m)gh]^1/2

------------ -------------------------------

2g(M+m) g(M+m)^3/2

???????????????????????????????????????????????.

4. A small block of superdense material has a mass M_e/2. It is situated at a height ?h? above the earth?s surface.(h<<R_e).

Find its speed when the height reduces to ?h?/2.

(M_e=6x 10²⁴ kg). Ans.(2gh/3)^1/2

???????????????????????????????????????????????.

5. What is radial equilibrium?

???????????????????????????????????????????????..

6. In both cases, 0=tan^-1 (a/g).

How to know whether cart is moving on an incline(with uniform velocity) or on a horizontal plane (accelerated)?

????????????????????????????????????????????..

True or False :
Silver fluoride is fairly soluble in water.

17.03.2008

Integrate the foll.(kindly give hint)

1) 1-x²

--------------

x(1-2x)

2) 1

---------

1-x⁴

3) ? (x²+1) [log(x²+1)- 2logx]

------------------------------------

x⁴

Which of the foll. is chiral?

Ans.1&2

08.02.2008(sent)

Physics

1. A uniform chain of mass M & length L is held vertically in such a way that its lower end just touches the horizontal floor.

The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length ?x? has reached the floor.

Ans.3Mgx/l

2.Two balls having masses m and 2m are fastened to two light strings of same length l. The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic.

(a) Find the velocities of the balls just after the collision..

(b) How high will the balls rise after the collision.

Ans.(a) Light ball?50gl/ towards left, heavy ball ?2gl /3 towards right.

(b) Light ball 2l, heavy ball l/9.

m 2m

ß-----------àß-----------------à

l l

3. A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is ?50 m? where ?m? is mass of one shell. If the muzzle velocity of the shells is 200m/s, what is the recoil speed of the car after the second shot? Neglect friction.

Ans. 200(1/49+1/48)m/s

4. A ball of mass is dropped onto a floor from a certain height. The collision is perfectly elastic. And the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval?

Ans. mg

5. The structure of a water molecule is shown in figure. Find the distance of the centre of mass of the molecule from the centre of oxygen atom.

O

104^o 0.96 x 10^-10 m

0.96 x 10-¹⁰ m

H H

6. 2 blocks A and B, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block A can slide is smooth. The block A is attached to a spring of spring constant 40N/m whose other end is fixed to a support 40cm above the horizontal surface. Initially, the spring is vertical and unstretched

when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take g=10m/s².(fig. below) [ Ans.1.5m/s]

7. A particle is projected with a speed of u at angle 0 with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an angle 0/2 with the horizontal?

[Ans. u² cos²0/gcos³(0/2)]

8. A car driver going at some speed v suddenly finds a wide wall at a distance r. Should he apply the brakes or turn the car in a circle of radius r to avoid hitting the wall?

9.A block of mass 2kg is pushed against a rough vertical wall with a force of 40 N . Coefficient of static friction being 0.5.Another horizontal force of 15N is applied on the block in a direction parallel to the wall . Will the block move? If yes, in which direction? If no find the frictional force exerted by the wall on the block. [Ans. moves at an angle of 53^o with the 15N force]

1. (exp)[(cos²x+cos⁴x+????..)logx] is a root of t²-8t+9,then tanx is

a)?3 b)?2 c)1 d)1/?2 ans.a)

2.(cos p-1)x²+(cos p)x+sin p=0 has real roots,then p belongs to

a)(0,?) b)(- ?,0) c)(- ?/2, ?/2) d)(0, ?) ans.d)

3) 6 dice are thrown. Probability that different nos. will turn up is

a)5/36 b)5/324 c)3/324 d)1/324 ans.a)

4) 12 balls are distributed among 3 boxes. The probability that first box contains 3 balls is

a)110/9 X (2/3)¹⁰ b)9/110 X (2/3)¹⁰ c)¹²C₃/12 X2⁹ d)¹²C₃/3¹²ans.a)

08.02.2008

Physics

1. A uniform chain of mass M & length L is held vertically in such a way that its lower end just touches the horizontal floor.

The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length ?x? has reached the floor.

Ans.3Mgx/l

2.Two balls having masses m and 2m are fastened to two light strings of same length l. The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic.

(a) Find the velocities of the balls just after the collision..

(b) How high will the balls rise after the collision.

Ans.(a) Light ball?50gl/ towards left, heavy ball ?2gl /3 towards right.

(b) Light ball 2l, heavy ball l/9.

O--------------------------------O

m 2m

ß-----------àß-----------------à

l l

3. A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is ?50 m? where ?m? is mass of one shell. If the muzzle velocity of the shells is 200m/s, what is the recoil speed of the car after the second shot? Neglect friction.

Ans. 200(1/49+1/48)m/s

4. A ball of mass is dropped onto a floor from a certain height. The collision is perfectly elastic. And the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval?

Ans. mg

5. The structure of a water molecule is shown in figure. Find the distance of the centre of mass of the molecule from the centre of oxygen atom.

O

104^o 0.96 x 10^-10 m

0.96 x 10-¹⁰ m

H H

6. 2 blocks A and B, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block A can slide is smooth. The block A is attached to a spring of spring constant 40N/m whose other end is fixed to a support 40cm above the horizontal surface. Initially, the spring is vertical and unstretched

when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take g=10m/s².(fig. below) [ Ans.1.5m/s]

7. A particle is projected with a speed of u at angle 0 with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an angle 0/2 with the horizontal?

[Ans. u² cos²0/gcos³(0/2)]

8. A car driver going at some speed v suddenly finds a wide wall at a distance r. Should he apply the brakes or turn the car in a circle of radius r to avoid hitting the wall?

9.A block of mass 2kg is pushed against a rough vertical wall with a force of 40 N . Coefficient of static friction being 0.5.Another horizontal force of 15N is applied on the block in a direction parallel to the wall . Will the block move? If yes, in which direction? If no find the frictional force exerted by the wall on the block. [Ans. moves at an angle of 53^o with the 15N force]

03.02.2008 (to be sent)

1. (exp)[(cos²x+cos⁴x+????..)logx] is a root of t²-8t+9,then tanx is

a)?3 b)?2 c)1 d)1/?2 ans.a)

2.(cos p-1)x²+(cos p)x+sin p=0 has real roots,then p belongs to

a)(0,?) b)(- ?,0) c)(- ?/2, ?/2) d)(0, ?) ans.d)

3) 6 dice are thrown. Probability that different nos. will turn up is

a)5/36 b)5/324 c)3/324 d)1/324 ans.a)

4) 12 balls are distributed among 3 boxes. The probability that first box contains 3 balls is

a)110/9 X (2/3)¹⁰ b)9/110 X (2/3)¹⁰ c)¹²C₃/12 X2⁹ d)¹²C₃/3¹²ans.a)

26.01.2008 (To be sent)

1.If (exp)(cos²x+cos⁴x+??????.)logx is a root of t2-8t-9=0, then tanx is

a)?3 b)?2 c)1 d)1/?2

Ans.a)

2. (cos p -1)x²+ (cos p) +sin p=0 has real roots, then p belongs to ????

a) (0,2?) b)(- ?,0) c)(- ?/2, ?/2) d)(0,?)

Ans.d)

3) x2-ax+b=0 and x2+bx-a=0 have a common root ,then a+b=o and a-b=1. Prove.

4)x²-2xcos0+1=0, then x²ⁿ-2xⁿcosn0+1=?

a) cos2n0 b)sin2n0 c)0 d)some real no.other than 0.

Ans.c)

5) If x=c is a root of order 2 of a polynomial f(x), then x=c is also a root of

a) f ? (x) b) f ??(x) c) f ???(x) d)none

Ans) a)

6)An n-digit no. is a positive no. with exactly n-digits. 900 distinct n-digit nos. are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible is

a)6 b)7 c)8 d)9

Ans. d)

26.01.2008 (To be sent)

1.If (exp)(cos²x+cos⁴x+??????.)logx is a root of t2-8t-9=0, then tanx is

a)?3 b)?2 c)1 d)1/?2

Ans.a)

2. (cos p -1)x²+ (cos p) +sin p=0 has real roots, then p belongs to ????

a) (0,2?) b)(- ?,0) c)(- ?/2, ?/2) d)(0,?)

Ans.d)

3) x2-ax+b=0 and x2+bx-a=0 have a common root ,then a+b=o and a-b=1. Prove.

4)x²-2xcos0+1=0, then x²ⁿ-2xⁿcosn0+1=?

a) cos2n0 b)sin2n0 c)0 d)some real no.other than 0.

Ans.c)

5) If x=c is a root of order 2 of a polynomial f(x), then x=c is also a root of

a) f ? (x) b) f ??(x) c) f ???(x) d)none

Ans) a)

6)An n-digit no. is a positive no. with exactly n-digits. 900 distinct n-digit nos. are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible is

a)6 b)7 c)8 d)9

Ans. d)