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

Options

A. `sqrt(2) R`
B. `(1 + sqrt(2))R`
C. `2(1 + sqrt(2))R`
D. `12 R`

Answer

C

Explanation

`v = 2sqrt(gR) , - R = v sin 45^@ t - 1/2 g t^2`
`t = sqrt((2R)/(g)) (1 + sqrt(2))`
`x = tv cos 45^@ = 2(1 + sqrt(2))R`.