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Q.

In order to raise a mass m a man ties it to a rope and passes the rope over a frictionless pulley. He climbs the rope with an acceleration 3g/2 relative to the rope. If the mass of the man is m/2 and the mass of the rope is negligible, the tension in the rope is

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a

3mg2

b

5mg3

c

7mg6

d

9mg7

answer is C.

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Detailed Solution

given amR= am-aR= 3g2; am =3g2-  aR as man and rope moving in oppsote direction  equation for the  man T-mg2=m2 am=m23g2-  aR  ;   T=5mg4-12maR----1 equation for the mass T-mg=maR----2 solving for T we get T=7mg6
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In order to raise a mass m a man ties it to a rope and passes the rope over a frictionless pulley. He climbs the rope with an acceleration 3g/2 relative to the rope. If the mass of the man is m/2 and the mass of the rope is negligible, the tension in the rope is