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 velocity given to the ball at point A so that it may hit the top of the building is

Options

A. (a) `sqrt(4gR)`
B. (b) `sqrt(2gR)`
C. (c) `sqrt(gR)`
D. (d) `sqrt(6gR)`

Answer

D

Explanation

Let t be the time taken by the ball from B to C.
`R=1/2"gt"^2`
`t=sqrt((2R)/(g))`
`2R=vsqrt((2R)/(g))`
`v=sqrt(2gR)`
Applying energy conservation at point A and B,
`1/2mv_0^2=1/2mv^2+mg2R`
`impliesv_0=sqrt(6gR)`