Question

Two blocks of mass $m_1$ and $m_2$ connected by a light string passing over a pulley $B$ are shown in the figure. The centre of pulley $B$ is connected to the floor by another light string passing over pulley $A$. Both the pulleys are massless. If $m_1=5\text{kg}$ and $m_2=10\text{kg}$, and a force of $300\text{N}$ acts on pulley $A$, then choose the correct option(s). (Take $g=10m/s^2$)

• A. Acceleration of $m_1$ will be $10{\text{m/s}}^2$
• B. Acceleration of $m_2$ will be $0{\text{m/s}}^2$
• C. Acceleration of $m_1$ will be $5{\text{m/s}}^2$
• D. Acceleration of $m_2$ will be $5{\text{m/s}}^2$

Answer 1

Answer: (B), (C)

Acceleration of $m_1$ will be $5{\text{m/s}}^2$

Step 1: Identify the number of strings passing over pulleys and draw FBD of masses $m_1$ and $m_2$
Step 2: From figure, $F=2T_2$ and $T_2=2T_1$
$\Rightarrow F=4T_1$
Step 3: $T_1=\frac{F}{4}=\frac{300}{4}=75\text{N}$
Step 4: Verify the motion of masses from FBD
$T_1>m_{1}g\left(50N\right);T_1<m_{2}g\left(100N\right)$
$\Rightarrow m_2$ is at rest as it will be on floor and $m_1$ moves upwards with acceleration
$a_1=\frac{T_1-m_{1}g}{m_1}=\frac{75-50}{5}=5{\text{m/s}}^2$