A ball is suspended from the top of a cart by a light string of length 1.0 m. The cart and the ball are initially moving to the right at constant speed V, as shown in figure I. The cart comes to rest after colliding and sticking to a fixed bumper, as in figure II. The suspended ball swings through a maximum angle 60°. The initial speed V is (take `g = 10 m//s^(2)`) (neglect friction)

Options

A. `sqrt(10) m//s`
B. `2sqrt(5)m//s`
C. `5sqrt(2)m//s`
D. `4m//s`

Answer

A

Explanation

As string does no work on the ball, energy conservation can be applied
`(1)/(2) mV^(2) = mg (L -L cos theta)`
`V = sqrt(2gL (1- cos theta))`
on putting values `V = sqrt(10) m//s`.