A bullet of mass m moving with a horizontal velocityu strikes a stationary wooden block of mass M suspended by a string of length L=50 cm. The bullet emerges out of the block with speed u/4. If M=6m, the minimum value of u so that the block can complete the vertical circle is (take `g =10ms^2`)

Options

A. `10 ms^(-1)`
B. `20 ms^(-1)`
C. `30 ms^(-1)`
D. `40 ms^(-1)`

Answer

D

Explanation

Let V be the speed of the block after the bullet emerges out of it. From conservation of momentum we have
`m u = MV + m(u/4) ,` which gives `V = (3 m u)/(4M)`
The minimum speed the block must have to complete the vertical circle is.
`V = sqrt(5 gl) implies (3 m u)/(4 M) = sqrt(5 g l) implies u (4M)/(3m) sqrt(5 gL)`
`= 4/3 xx 6 xx sqrt(5 xx 10 xx 0.5) = 40 ms^(-1)`