Question

Two blocks 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. The coefficient of 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?

• A. $\frac{M_{2}-M_{1}}{\mu}$
• B. $\frac{M_{2}}{\mu}-M_{1}$
• C. $M_{2}-\frac{M_{1}}{\mu}$
• D. $(M_{2}-M_{1})\mu$

Answer 1

Answer: (B)

For the equilibrium of block of mass $M_{1}:$
Frictional force, f = tension in the string, T
where $T=f =\mu (m+M_{1})gt .....(i)$
For the equilibrium of block of mass $M_{2}:$
$T=M_{2}g .....$(ii)
From (i) and (ii) $\mu(m+M_{1})g=M_{3}g$
$m=\frac{M_{2}}{\mu}-M_{1}$