Question

In the arrangement shown, the pulleys, strings and the spring balance, all are ideal. If $m_{1}>m_{2}$ , then the reading of the spring balance is

• A. $m_{1}-m_{2}$
• B. $\frac{1}{2}\left(m_{1} + m_{2}\right)$
• C. $\frac{4 m_{1} m_{2}}{m_{1} + m_{2}}$
• D. $\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}$

Answer 1

Answer: (D)

The acceleration of the system $= \left(\frac{\left(\text{m}\right)_{1} - \left(\text{m}\right)_{2}}{\left(\text{m}\right)_{1} + \left(\text{m}\right)_{2}}\right) \text{g}$ and hence the tension T in the string is $\left(\frac{\left(2 \text{m}\right)_{1} \left(\text{m}\right)_{2}}{\left(\text{m}\right)_{1} + \left(\text{m}\right)_{2}}\right) \text{g}$
The reading of the spring balance is T (in units of force) and T/g(in units of mass).