Question

Two masses $M_{1}=5\, kg$ and $M_{2}=10\, kg$ are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When the masses are released, then the acceleration of the masses will be

• A. $g$.
• B. $g / 2$
• C. $g / 3$
• D. $g / 4$

Answer 1

Answer: (C)

Since $M_{2}>M_{1},$ therefore $M_{2}$ moves downwards and $M_{1}$ moves upwards with an acceleration $a$ as shown in the figure. ummellyme

The equation of motion for $M_{1}$ is, $T-M_{1} g=M_{1} a \ldots( i )$
Free body diagram of $M_{2}$,
The equation of motion for $M_{2}$ is
$M_{2} g-T=M_{2} a$
Adding $(i)$ and $(ii)$ , we get
$a=\frac{\left(M_{2}-M_{1}\right) g}{M_{2}+M_{1}}=\frac{(10-5) g}{(10+5)}=\frac{g}{3}$