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In the arrangement shown below, pulleys ...

In the arrangement shown below, pulleys are mass-less and friction-less and threads are in-extensible. Block of mass `m_(1)` will remain at rest if :

A

`(1)/(m_(1)) = (1)/(m_(2)) + (1)/(m_(3))`

B

`m_(1) = m_(2) + m_(3)`

C

`(4)/(m_(1)) = (1)/(m_(2)) + (1)/(m_(3))`

D

`(6)/(m_(1)) = (1)/(m_(2)) + (2)/(m_(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
`m_(1)` will be at rest if `2T = m_(1) g implies T = (m_(1) g)/(2)`
As shown in figure `a = ((m_(2) - m_(2))g)/((m_(2) + m_(3)))`
For `m_(2) : m_(2) g - T = m_(2) a implies m_(2) g - (m_(1) g)/(2) = m_(2) [((m_(2) - m_(3))g)/((m_(2) + m_(3)))]`
`implies m_(2) [1- ((m_(2) - m_(3))/(m_(2) + m_(3)))] = (m_(1))/(2)`
`implies (m_(2) (2m_(3)))/(m_(2) + m_(3)) = (m_(1))/(2) implies (4)/(m_(1)) = (1)/(m_(2)) + (1)/(m_(3))`
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