Question

A block of mass $1\text{kg}$ is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown. Another block of $1\text{kg}$ is connected to the other end of the string, the acceleration of the system is (coefficient of friction $\mu =0.4)$

• A. $0.8\text{g}$
• B. $0.4\text{g}$
• C. $0.3\text{g}$
• D. zero

Answer 1

The correct option is C $0.3\text{g}$

Here by the string constraint we can say that both block will have same magnitude of acceleration.

By the free body diagram


We know that the acceleration of the system is, here the applied force will be $mg$ and the opposing force will be $f=\mu N=\mu mg$

$a_{sys}=\frac{\text{applied force}-\text{opposing force}}{\text{total mass}}$

$a_{sys}=\frac{mg-\mu mg}{2m}=0.3g{\text{m/s}}^2$

Hence option C is the correct answer