Question

Two blocks of masses 3 m and m are connected by a massless and inextensible cord passing over a massless and frictionless pulley. Calculate the magnitude of acceleration of the centre of mass of the system when the blocks are allowed to accelerate. $\left(g=10\, ms ^{-2}\right)$

• A. $0.5 \,ms ^{-2}$
• B. $1.5\, ms ^{-2}$
• C. $2.5 \,ms ^{-2}$
• D. $3.5 \,ms ^{-2}$

Answer 1

Answer: (C)

$a=\left(\frac{m_{2}-m_{1}}{m_{2}+m_{1}}\right) g$
Here $m_{2}=3 m, m_{1}=m$
$\Rightarrow a_{3 m}=\left(\frac{3 m-m}{3 m+m}\right) g=\frac{g}{2}$ downward
$a_{m}=\frac{g}{2}$ upward
$a_{ cm }=\frac{(3 m)\left(+\frac{g}{2}\right)+(m)\left(-\frac{g}{2}\right)}{3 m+m}=\frac{m g}{4 m}=\frac{g}{4}$ downward
$=\frac{10}{4}=2.5 \,ms ^{-2}$