Question

Work done by a simple pendulum in one complete oscillation is:
1. Zero
2. \(2\pi \sqrt{\frac{l}{g}}\)
3. Infinity
4. None of these

Answer 1

Correct Answer - Option 1 : Zero

CONCEPT:

• Simple pendulum: A point mass attached to a light inextensible string and suspended from fixed support is called a simple pendulum. The vertical line passing through the fixed support is the mean position of a simple pendulum. 
• The total work done by the force is equal to the product of the magnitude of applied force and the distance travelled by the body.

The work done is given as:

W = F × d.

• In this case, the force exerting on the block is constant, but the direction of force and direction of displacement influenced by this force is different. Here, force F reacts at an angle θ to the displacement d.

W = (|F| cosθ) |d|

• We know that work done is defined as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement.

EXPLANATION:

• One of the force is gravity. The force of gravity acts in a downward direction and does work upon the pendulum bob. At all points in the trajectory of the pendulum bob, the angle between the force of tension and its direction of motion is 90°.
• Thus, the force of tension does not do work upon the bob.
• Hence option 1 is the answer.

• The oscillatory motion of a simple pendulum: Oscillatory motion is defined as the to and fro motion of the pendulum in a periodic fashion and the centre point of oscillation known as equilibrium position.
  • The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by "T".
  • The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the equilibrium position to one side,
  • Length of a simple pendulum: It is defined as the distance between the point of suspension to the centre of the bob and is denoted by "I"
• Work done: Work done is elaborated in such a way that it includes both forces exerted on the body and the total displacement of the body.
  • This block is preceded by a constant force F. The purpose of this force is to move the body a certain distance (d) in a straight path in the direction of the force.