Question:

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

Updated On: Jun 2, 2024
  • $M g \frac{d}{4}$
  • $3 M g \frac{d}{4}$
  • $-3 M g \frac{d}{4}$
  • $ Mgd $
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The Correct Option is C

Solution and Explanation

When the block moves vertically downward with acceleration $\frac{g}{4}$ then tension in the cord $T=M\left(g-\frac{g}{4}\right)=\frac{3}{4} M g$ Work done by the cord $=F \cdot s=F s \cos \theta$ $=T d \cos 180^{\circ}$ $=\left(-\frac{3}{4} M g\right) \times d$ $=-3 M g \frac{d}{4}$
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Questions Asked in AIIMS exam

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Concepts Used:

Work

Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.

Work Formula:

W = Force × Distance

Where,

Work (W) is equal to the force (f) time the distance.

Work Equations:

W = F d Cos θ

Where,

 W = Amount of work, F = Vector of force, D = Magnitude of displacement, and θ = Angle between the vector of force and vector of displacement.

Unit of Work:

The SI unit for the work is the joule (J), and it is defined as the work done by a force of 1 Newton in moving an object for a distance of one unit meter in the direction of the force.

Work formula is used to measure the amount of work done, force, or displacement in any maths or real-life problem. It is written as in Newton meter or Nm.