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Question: Two weights w1 and w2 are suspended from the ends of a light string passing over a smooth fixed pul...

Two weights w1 and w2 are suspended from the

ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration g , the tension in the string will be-

A

4w1w2w1+w2\frac { 4 w _ { 1 } w _ { 2 } } { w _ { 1 } + w _ { 2 } }

B

2w1w2w1+w2\frac { 2 \mathrm { w } _ { 1 } \mathrm { w } _ { 2 } } { \mathrm { w } _ { 1 } + \mathrm { w } _ { 2 } }

C

w1−w2w1+w2\frac { w _ { 1 } - w _ { 2 } } { w _ { 1 } + w _ { 2 } }

D

w1w22(w1−w2)\frac { \mathrm { w } _ { 1 } \mathrm { w } _ { 2 } } { 2 \left( \mathrm { w } _ { 1 } - \mathrm { w } _ { 2 } \right) }

Answer

4w1w2w1+w2\frac { 4 w _ { 1 } w _ { 2 } } { w _ { 1 } + w _ { 2 } }

Explanation

Solution

T=2 m1 m2( g+a)m1+m2\mathrm { T } = \frac { 2 \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } ( \mathrm {~g} + \mathrm { a } ) } { \mathrm { m } _ { 1 } + \mathrm { m } _ { 2 } } ,

T = 2w1g⋅w2g(g+g)w1g+w2g\frac { 2 \frac { w _ { 1 } } { g } \cdot \frac { w _ { 2 } } { g } ( g + g ) } { \frac { w _ { 1 } } { g } + \frac { w _ { 2 } } { g } } ̃ T = 4w1w2(w1+w2)\frac { 4 w _ { 1 } w _ { 2 } } { \left( w _ { 1 } + w _ { 2 } \right) }