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A horizontal cylinder is fixed, its inne...

A horizontal cylinder is fixed, its inner surface is smooth and its radius is R. A small block is initially at the lowest point. The minimum velocity that should by given to the block at the lowest point, so that it can just cross the point P is u then

A

If the block moves anti clockwise then `u = sqrt(3.5 gR)`

B

If the block moves anti clockwise then `u = sqrt(3 gR)`

C

If the block moves clockwise then `u = sqrt(3.5 gR)`

D

If the block moves clockwise then `u = sqrt(5 gR)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`N = (mu^(2))/(R) + mg (3 cos theta - 2)`, at `theta = 120^(@) N`
`= 0 rArr N = (m u^(2))/(R) + mg (3 cos 120^(@) - 2) =0`
`rArr u = sqrt(3.5 gR)`
If the block is moving clockwise, then to cross the point P, the block has to cross the highest point, so to cross the highest point
`= sqrt(5gR)`.
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