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1) pick the correct statements(multiple ans)
a)avg speed of a particle in a given time is never less than the magnitude of the avg. velocity.
b)it is possible to have a situation in which |dv/dt|
0 but d|v|/dt =0.
c)the avg.velocity of a particle is 0 in a time interval.it's possible that the instantaneous velocity is never =0 in this interval.
d)the avg velocity of a particle moving on a straight line is 0 in a time interval.it's possible that the inst.velocity is never 0 in this interval.
2)what is tensor?
(noment of inertia is a tebsor.scalars have tensor rank=0 and vectors have tensor rank as 1)
3)12 coplanar forces(all equal in magnitude)maintain a body equilibrium,then the angle between any two adjacent forces is___________
4)at what angle should two unit vectors be inclined so that their resultant is also a unit vector?
5)the sum.difference,and cross product of two vectors A and B are mutually perpendicular if:
a) A nd B are perpendicular to each other and |A|=|B|
b)A and B are perpendicular to each other
c)A and B are perpendicular but magnitudes are arbitrary
d)|A|=|B| and their direction are arbitrary.
please give ur reasons and workings also.
Comments (9)
= 1 
= -1 option a,b,c are correct
a- u know that distance is always greater than displacement
therefore a is correct
b- Idv/dtI is modulus of acceleration and IdvI/dt is rate of change of
speed . the given cond is true in uniform circular motion
c- a particle in circular motion after one rotation has average
velocity 0 but inst velocity is never zero
d- for zero average velocity particle shud come back to initial point
and in straight line motion it means that particle have to reverse its
direction of motion .at the point of reversal its inst velocity will be 0
OPTION B IS NOT CORRECT BECAUSE IF VELOCITY CHANGES THEN MOD OF ACCN MAY BE SOME NUMBER IN THE SAME SITUATION VELOCITY AT ANY INSTANT MAY BE ZERO.AS IF IN PROJECTILE WHEN IT REACHES HIGHEST POINT.ITS DIFFERENT IN DIFFERENT CONDITIONS LIKE IN PROJECTILE MOTION AND UNIFORM CIRCULAR MOTION.
OPTION C IS TRUE.THE DIRECTION OF VELOCITY DECIDES THAT.
D IS ALSO TRUE
SOLUTION TO Q-1.
STATEMENT-1
We know that -
Since Distance travelled is always greater than or equal to displacement for a fixed interval of time, Average speed is always greater than or equal to average velocity.
STATEMENT-1 IS TRUE.
STATEMENT-2-
I cannot help u in this.
STATEMENT -3-
Average velocity can be zero even when displacement is zero.
Hence, when a body moves with certain velocity and returns to its original position, then its average velocity is zero, but its instantaneous velocity is never zero.
Hence,STATEMENT -3 IS TRUE
STATEMENT-4
When a body is moving in a straight line, then average velocity is zero only when it is not in motion, i.e., displacement is zero. Hence, instantaneous velocity will be zero.
STATEMENT-4 IS FALSE
HOPE THIS HELPS YOU
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3) If n equal forces keep the body in equilibrium, then the angle between any two adjacent forces must be (360/n)
Hence, the answer to this question is 360/12 = 30o
Hope this helps
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