NEET Physics Question - Oscillation

Assertion (A): If PE of a particle executing SHM is given by \(U = x^2 - 10x + 27\), then it is executing SHM about \(x = 5\).

Reason (R): At mean position, restoring force is zero.

(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(3) (A) is true but (R) is false

(4) Both (A) and (R) are false

Solution:

Assertion (A): Given \(U = x^2 - 10x + 27 = (x-5)^2 + 2\). For SHM, \(U = \frac{1}{2}k(x-x_0)^2 + U_0\). Comparing, mean position \(x_0 = 5\). So (A) is true. Reason (R): The restoring force \(F = -\frac{dU}{dx}\). At equilibrium (mean) position, \(F=0\). So (R) is true. (R) does not explain (A).

Rankers Physics

SHM Potential Energy and Mean Position

Solution:

Leave a Reply Cancel reply