IAS Physics Sample Questions ans ans III (Read 7 times)

1. Two particles m1 and m2 are connected by a light elastic string of natural length lo and are placed on a smooth horizontal table with separation between m1 and m2 as lo. m2 is projected with a velocity vo along the table at right angles to the string. Show that the max length l of the particle is given by: l2(l-lo)=m1m2vo2(l+lo)/k(m1+m2) where k is force const of string

2. Two equal particles are attached to the end of a light rod and a 3rd equal particle is connected by an inextensible string to a point on the rod at distance a and b from its ends. The latter particle is projected at right angles to the rod with a velocity vo. Show that when the string becomes taut the velocity of the particle is changed to v1=vo(a2+b2)/2(a2+ab+b2) and that the rod begins to turn with angular velocity (a-b/a2+b2)v1.

3. A rod of length 2a and mass M is in motion in a horizontal plane with speed u at right angle to its length when it collides with a small elastic sphere of equal mass whose center lies in the same plane. If the sphere is free to move, Prove that angular velocity acquired by the rod cannot exceed (1+e)uÖ6/4a.