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A smooth massless string passes over a s...

A smooth massless string passes over a smooth fixed pulley. Two masses `m_(1) and m_(2) (m_(1) gt m_(2))` are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The acceleration of the two masses is

A

`(m_(1) + m_(2))g`

B

`((m_(1) - m_(2)))/(m_(1) + m_(2))g`

C

`(m_(1) - m_(2))g`

D

`((m_(1) + m_(2))^(2))/(m_(1) - m_(2))g`

Text Solution

Verified by Experts

If a is the acceleration of the two masses and T is the tension in the two sides of the string, then
`m_(1)g -T = m_(1) a " " `(1)
` T - m_(2)g = m_(2)a" "`…(2)
Now from equations (1) and (2), we get,
a = `((m_(1) - m_(2)))/(m_(1) + m_(2))g `
Therefore, total external force
` = (m_(1) + m_(2)) a = (m_(1) - m_(2))g`
The option c is correct.
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