Question

Assertion : The graph of total energy of a particle in SHM with respect to position is a straight line with zero slope.
Reason : Total energy of particle in SHM remains constant throughout its 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

Answer: (A)

If both assertion and reason are true and reason is the correct explanation of assertion.

We know that, total energy of the particle executing SHM is constant.

$KE=\frac{1}{2}m{v}^2=\frac{1}{2}m{w}^2(A^2-x^2)[x=displacement,A=constant=amplitude]$

$PE=\frac{1}{2}m{w}^2{x}^2$

$E=\frac{1}{2}m{w}^2{A}^2=constant$

See the figure. Option $A$ is correct answer.