IAS Physics Questions (Read 5 times)

1. A cube rests on a rough plane of inclination q (< p/4) with 2 of its upper and two of its lower edges horizontal. A rope is attached to the midpoint of its upper most edge and is pulled parallel to the greatest slope of the plane. Show that it will be impossible to drag the cube without upsetting it if the coefficient of friction exceeds (1-tan q)/2


2.  [Figure for question 6]A uniform rod of length 2a, mass m is set in motion by a sudden blow J acting at A and inclined at q to rod as shown. Find velocity of A of rod immediately after the impact and Prove that energy communicated is J2(1+3sin2q)/2m
A small block of mass m is placed inside a hollow cone rotating about a vertical axis with angular velocity w as in the figure. The semivertical angle of the cone is q and the coefficient of friction between the cone and the block is m. If the block is to remain at a constant height h above the apex of the cone, what are the maximum and minimum values of w?
Physics Questions uniform thin rod AB
A uniform thin rod AB of mass 3m and length 2a is free to rotate in a horizontal plane about a smooth fixed vertical axis which passes through the midpoint O of the rod. Two small smooth rings each of mass m are free to slide on the rod. At time t=0 the rings are on the opposite side of O and are at a distance a/2 from O. The rod is then given an initial angular velocity 2Ög/a, the rings being initially at rest relative to the rod.

   1. Show that when the rings are about to slip off the rod its angular velocity is Ög/a.
   2. Find the speed of either ring at this instant.
   3. If the point O is at a height a above the horizontal plane show that the distance between the points where the ring strikes the plane is 2aÖ(6 + 2Ö3).