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Question

A circular pulley of mass M and radius R, is hinged at the centre. A long string is wound over this disc and two bodies of mass m1 and m2 are attached at its free ends. Now the bodies are released. Find the acceleration of each body.

A
2[m1m2]gM+(m1+m2)
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B
[m1m2]gM+2(m1+m2)
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C
2[m1m2]gM+2(m1+m2)
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D
[m1m2]gM+(m1+m2)
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Solution

The correct option is C 2[m1m2]gM+2(m1+m2)
Pulley:
τ=T1RT2R
Iα=(T1T2)R
12MR2×aR=(T1T2)R
Ma2=T1T2
From (i) and (ii)
T1T2=m1gm1am2gm2a
Ma2+(m1+m2)a=(m1m2)g
a=2(m1m2)gM+2(m1+m2)

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