Question

Assertion: Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the latter motion occurs.
Reason: Simple harmonic motion is a uniform motion.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer 1

In simple harmonic motion, we have a to and fro periodic motion about a mean position. A uniform motion is that motion in which the velocity of the moving object remains the same. A simple harmonic motion is characterized by change in velocity during the to and fro motion.

Complete answer:
A body is said to be executing a simple harmonic motion if it is moving to and fro about a point in a periodic manner. For example, in the case of a simple pendulum displaced slightly from its mean position executes a simple harmonic motion. We will consider this example for understanding the simple harmonic motion. When the pendulum executes simple harmonic motion then the to and fro periodic motion can be visualized as a projection of uniform circular motion of the pendulum bob on the diameter of the circle. Therefore, we can say that the assertion is true.
The reason says that the simple harmonic motion is a uniform motion. This statement is in itself incorrect and also not the explanation of the assertion. In actuality the simple harmonic motion is not a uniform motion. When a pendulum oscillates about its mean position, its kinetic energy and hence, the velocity keeps changing. The velocity at the extreme positions is zero and is maximum at the mean position of the pendulum.

Hence, we can say that the correct answer is option C.

Note:
The kinetic energy and the potential energy of the pendulum keep changing during the oscillations of the pendulum. The kinetic energy of the bob is minimum at the extreme position but the potential energy is maximum at the extreme position. The kinetic energy increases as the bob moves towards the mean position while the potential energy decreases keeping the total energy constant.