Ques. 1AIPMT 2003
A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is
- 2(u2 - gl)
- u2 - gl
- u - u2 - 2gl
- 2gl
Answer
(1) 2(u2 - gl)
Solution
From the lowest point to the horizontal position the stone rises through height l, so by conservation of mechanical energy
12mu2 = 12mv2 + mgl
v2 = u2 - 2gl
At the lowest point the velocity is horizontal and at the horizontal position it is vertical, so u v and
| v| = u2 + v2 = u2 + u2 - 2gl = 2(u2 - gl)
Answer: (1)