Question

Two bodies of masses $m_{1}$ and $m_{2}$ are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$, then tension in the string will be

• A. $\frac{3 m_{1} m_{2}}{m_{1}+m_{2}} g$
• B. $\frac{m_{1}+m_{2}}{4 m_{1} m_{2}} g$
• C. $\frac{2 m_{1} m_{2}}{m_{1}+m_{2}} g$
• D. $\frac{m_{1} m_{2}}{m_{1}+m_{2}} g$

Answer 1

Answer: (A)

Writing equation from the reference frame of pulley
$\frac{3 m_{1} g}{2}-T=m_{1} a$ ...(i)
$T-\frac{3 m_{2} g}{2}=m_{2} a$ ...(ii)
Add (i) and (ii)
$\frac{3 g}{2}\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right)=a$
Use a in eq. (i) or (ii)
Solving $T=\frac{3 m_{1} m_{2}}{m_{1}+m_{2}} g$