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 plased 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)`:
friction force `f =` tension in the string T
where`T = f = mu(m + M_(1))g`
For the equilkibrium of block of mass `M_(2)`
`T = M_(2)g`
From Eqs (i) and (ii)we get`mu(m +M_(1))g = M_(2)g`
`m = (M_(2))/(mu) - M_(1)`