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A small ball is given some velocity at p...

A small ball is given some velocity at point A towards right so that it moves on the semicircular track and does not leave contact up to the highest point B. After leaving the highest point B, it falls at the top of a building of height R and width `x(xlt lt 2R)`. (All the surfaces are frictionless).

The horizontal distance of the ball from the foot of the builing where the ball strikes the horizontal ground will

A

`sqrt(4 gR)`

B

`sqrt(2 gR)`

C

`sqrt(7 gR)`

D

`sqrt(6 gR)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let t be the time taken by the ball from B to C.
`R = 1/2 gt^2 implies t = sqrt((2R)/(g)) , 2R = vsqrt((2R)/(g)) = sqrt(2 gR) = v`.
Applying energy conservation at point A and B. `1//2 mv_(0)^2 = 1/2 mv^2 + mg 2R`.
`v_(0) = sqrt(6 gR)`.
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