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Asked by maps.stuti | 03 Jan, 2022, 08:19: AM
Tension forces acting on string at various points are shown in figure.

If the 4 kg block moves down Δl downwards , length of string EF increases by Δl ,  length between E and A decreases by Δl and length between O and A increases by Δl .

Hence length between B and C decreases by Δl .

Hence magnitude of acceleration of 4 kg block and magnitude of acceleration of 2 kg block are equal.

Free body diagram for 2 kg block on inclined surface and free body diagram of 4 kg block are shown in figure.

By applying Newton's law to the 2 kg block, we get

T - ( 2 g sin30 ) = 2 a

T - g = 2a   ..............................(1)

where a is acceleration of the system

By applying Newton's law to the 4 kg block , we get

4g - 2T = 4a ................................(2)

By multiplying eqn.(1) by 2 and adding eqn.(2) , we eliminate tension T and we get

acceleration a  = (1/4) g

If we consider acceleration due to gravity g = 10 m/s2  , then acceleration a = 5/2 m/s2
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