Explain propagation of errors in the difference of two quantities and also in the division of two quantities.

The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k = 1)

Convert the vector \(\vec { r } =3\hat { i } +2\hat { j } \) into a unit vector.

A particle moves in a circle of radius 4.0 cm clockwise at constant speed of 2 cms^-1. If \(\hat x\) and \(\hat y\) are unit acceleration vectors along x-axis and y-axis respectively (in cms^-2 ), find the acceleration of the particle at the instant half way between P and Q.

A car takes a turn with velocity 50 ms^-1 on the circular road of radius of curvature 10m. calculate the centrifugal force experienced by a person of mass 60kg inside the car?

What happens to the object at rest if
(i) f_s = 0 
(ii) fs = Fext 
(iii) fs = max.

A bullet of mass 25 g moving with a velocity of 400 ms^-1 strikes a cardboard and goes out from the other end with a velocity of 300 ms^-1, find out the work done in passing through the cardboard.

If a particle elastically collides obliquely with a particle of same mass at rest then show that they move perpendicular to each other after collision.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad/s. The radius of the cylinder is 0.25m. Calculate the kinetic energy associated with the rotation of the cylinder.

Two particles P and Q of mass 1 kg and 3 kg respectively start moving towards each other from rest under mutual attraction. What is the velocity of their center of mass?

Explain the variation of g with altitude.