Question

A weightless string passes through a slit over a pulley. The slit offers frictional force/to the string. The string carries two weights having masses m₁and m₂where m₂>m ₁, then acceleration of the weights is

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

Answer 1

Answer: (A)

$\frac{\left( m_{2} - m_{1} \right)g - f}{m_{1} + m_{2}}$

Answer 2

Here m₂g – T₂ = m₂a, …………. (i)

and T₁ – m₁g = m₁a ……….. (ii)

Also (T₁ + f) – T₂= 0 ……… (iii)

( tension below the slit is T₂ and above the slit is T₁).

Solving the above equations, a = $\frac{\left( m_{2} - m_{1} \right)g - f}{m_{1} + m_{2}}$