Question

A block of mass 10 kg is placed on a horizontal surface is connected by a cord passing over a frictionless pulley to a hanging block of mass 10 kg. If the coefficient of friction between the block and the surface is 0.5 and g = 10 m/s^2, then find the accleration of the system.

• A. 1.5
• B. 0.5
• C. 2.5
• D. 0.3

Answer 1

The correct option is C 2.5

For mass $A:T-\mu m_{1}g=m_{1}a$

$\to T=m_{1}a+\mu m_{1}g\to \left(1\right)$

For mass $B:m_{2}g-T=m_{2}a$

$\to T=m_{2}g-m_{2}a\to \left(2\right)$

From $\left(1\right)$ and$\left(2\right)$

$m_{1}a+\mu m_{1}g=m_{2}g-m_{2}aa=\frac{(m_2-\mu m_1)g}{m_1+m_2}a=\frac{(10-0.5\times 10)10}{10+10}$

Thus $a=2.5m/s^2$