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A mass m hangs with the help of a string...

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m if the string does not slip on the pulley, is

A

g

B

`(2)/(3)g`

C

`(g)/(3)`

D

`(3)/(2)g`

Text Solution

Verified by Experts

The correct Answer is:
B
If `alpha` be the angular acceleration then
`((1)/(2)mR^(2)+mR^(2))alpha=mg.R`
`therefore (3)/(2)mR^(2)alpha=mgR`
`therefore alphaR=((2)/(3))g`
`therefore` Acceleration .a. of the mass m is `((2)/(3))g`.
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