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NEET PHYSICSMedium

A cord is used to lower vertically a block of mass MM by a distance dd with constant downward acceleration g4\frac{g}{4}. Work done by the cord on the block is:

A

Mgd4\frac{Mgd}{4}

B

3Mgd4\frac{3Mgd}{4}

C

3Mgd4-\frac{3Mgd}{4}

D

MgdMgd

Step-by-Step Solution

Let the tension in the cord be TT. The block is moving downwards with a constant acceleration a=g4a = \frac{g}{4}. Applying Newton's second law of motion to the block in the downward direction: MgT=MaMg - T = Ma T=M(ga)=M(gg4)=3Mg4T = M(g - a) = M\left(g - \frac{g}{4}\right) = \frac{3Mg}{4}

The force exerted by the cord (tension TT) is directed vertically upwards, while the displacement dd is directed vertically downwards. The angle between the force and displacement vectors is θ=180\theta = 180^\circ. The work done by the cord on the block is given by: W=Tdcos180=TdW = Td \cos 180^\circ = -Td W=(3Mg4)d=3Mgd4W = -\left(\frac{3Mg}{4}\right)d = -\frac{3Mgd}{4}

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