Question:

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

Updated On: Jun 2, 2024
  • Mgd4M g \frac{d}{4}
  • 3Mgd43 M g \frac{d}{4}
  • 3Mgd4-3 M g \frac{d}{4}
  • Mgd Mgd
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The Correct Option is C

Solution and Explanation

When the block moves vertically downward with acceleration g4\frac{g}{4} then tension in the cord T=M(gg4)=34MgT=M\left(g-\frac{g}{4}\right)=\frac{3}{4} M g Work done by the cord =Fs=Fscosθ=F \cdot s=F s \cos \theta =Tdcos180=T d \cos 180^{\circ} =(34Mg)×d=\left(-\frac{3}{4} M g\right) \times d =3Mgd4=-3 M g \frac{d}{4}
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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.