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Question

A cat of mass m=1 kg climbs on a rope hung over a light frictionless pulley as shown in the figure. A mass M=2m lies on a smooth horizontal plane. What is the tension of the rope (in N) when the cat moves upwards with an acceleration a=2 m/s2 relative to the rope? (take g=10 ms2)

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Solution

acat/rope=acataRope=(2a) upwards
Therefore, from FBD
Tmg=m(2a)......(1)

Again,
2T=2×a2.......(2)
a=2T
Put value of 'a' in eq....(1), we get
T1×10=1(22T)
T+2T=12
3T=12
T=4 N

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