A smooth rope of mas `m` and length `L` lies in a heap on a smooth horizontal floor, with one end attached to a block of mass `M`. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude `V_(0)` as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance `x` from point `P` as shown in figure `-2( P` is a point on the rope which has just started to move at the given instant `)`, choose correct options for next three question.

The speed of block of mass `M` is

Options

A. `(mV_(0))/((M+(m)/(L)x))`
B. `(MV_(0))/((M+(m)/(L)x))`
C. `(m^(2)V_(0))/(M(M+(m)/(L)x))`
D. `(M^(2)V_(0))/(m(M+(m)/(L)x))`

Answer

B

Explanation

The mass of moving material is `M+(m)/(L)x`
From conservation of momentum `MV_(0)=(M+(m)/(L)x)V`
`:. `Velocity of moving block and moving rope is
`V=(MV_(0))/(M+(m)/(L)x)`