A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60 with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is m. [figure]
- 15
- 2 - 35
- 35
- 2 + 35
Answer
(1) 15
Solution
Speed of A at the lowest point (fall of height l(1 - 60 ) with l = 1 m):
v2 = 2gl(1 - 60 ) = 2g(1) ( 12 ) = g
Elastic collision between equal masses: the velocities are exchanged, so B moves off with vB = g and A stops.
To go round the track up to Q (beyond the top), B must just cross the highest point, where vtop = gR; this needs vB = 5gR at the bottom.
5gR = g
R = 15 m
Answer: (1)