Two block of masses `M_(1) and M_(2)` are connected with a string passing over a pulley as shown in figure The block `M_(1)` lies on a horizontal surface friction between the block `M_(1)` and the horizontal surface is `mu` The system accelerates. What additional mass `m` should be placed on the block `M_(1)` so that the system does not accelerate?

Options

A. `(M_(2)-M_(1))/(mu)`
B. `M_(2)/(mu)-M_(1)`
C. `M_(2)-M_(1)/(mu)`
D. `(M_(2)-M_(1))mu`

Answer

B

Explanation

For the equilibrium of block of mass `M_(1)` :
Frictional force, `f` = Tension in the string, `T`
where `T=f`

`mu(m+M_(1))g=M_(2)g`
`T=M_(2)g`
From (i) and (ii) `mu(m+M_(1))g=M_(2)g`
`m=(M_(2))/(mu)-M_(1)` .