Question

Two weights $W _ { 1 }$ and $W _ { 2 }$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration g, the tension in the string will be

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

Answer 1

Answer: (A)

$\frac { 4 W _ { 1 } W _ { 2 } } { W _ { 1 } + W _ { 2 } }$

Answer 2

When the system is at rest tension in string

$T = \frac { 2 m _ { 1 } m _ { 2 } } { \left( m _ { 1 } + m _ { 2 } \right) } g$

If the system moves upward with acceleration g then $T = \frac { 2 m _ { 1 } m _ { 2 } } { m _ { 1 } + m _ { 2 } } ( g + g )$ $= \frac { 4 m _ { 1 } m _ { 2 } } { m _ { 1 } + m _ { 2 } } g$ or $T = \frac { 4 w _ { 1 } w _ { 2 } } { w _ { 1 } + w _ { 2 } }$