Question

Two blocks of masses $M_1=4$kg and $M_2=6$kg are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure. The coefficient of friction between the block $M_1$ and the horizontal surface is $0.4$. When the system is released, the masses $M_1$ and $M_2$ start accelerating. What additional mass m should be placed over $M_1$ so that the masses $(M_1+m)$ slide with a uniform speed?

• A. $12$ kg
• B. $1$kg
• C. $10$ kg
• D. $8$kg

Answer 1

Answer: (A)

$12$ kg

For uniform motion of mass $M_2$-

$T=M_{2}g$

For uniform motion of $(M_1+m)$-

$T=f$

And, $f\le \mu N=\mu (M_1+m)g$

$⟹\mu (M_1+m)g\ge M_{2}g$

$⟹m\ge \frac{M_2}{\mu }-M_1$

$⟹m\ge \frac{6}{0.4}-4$

$⟹m\ge 11kg$

Hence, $m=12kg$