A bullet of mass m moving with velocity `upsilon_(1)` strikes a suspended wooden block of mass M as shown in the figure and sticks to it. If the block rises to a height y. the initial of the bullet is

Options

A. ` sqrt( 2gh ) `
B. ` (M+m)/( m) sqrt( gh ) `
C. ` ( m )/( M+m) 2gh `
D. ` (M+m)/( M) sqrt( 2gh) `

Answer

A

Explanation

Initial K.E. of block when bullet strikes to it
` = (1)/(2) (m + M) V^(2) `
Due to this K.E. block will rise to a height h.
Its potential energy = ( m+M) gh
By the law of conservation of energy
` (1)/(2) (m+ M) V^(2) = ( m +M) gh " " therefore V = sqrt(2gh) `