Physics - NLM Question with Solution | TestHub

In the cart's (non-inertial) frame a pseudo force ma acts opposite to the cart's acceleration. The string settles at a constant angle where:

$$\tan \theta =\frac{ma}{mg}=\frac{a}{g}$$

(A) Constant horizontal acceleration gives a constant angle - correct.

(B) With a spring instead of a string, the same static force balance applies once oscillations die out, so the same constant angle results - correct.

(C) On the incline the cart moves with constant speed, i.e. a = 0. The string hangs vertically: a constant angle - correct.

(D) Coming down a smooth incline, the cart's acceleration g sin$\theta$ along the plane is constant, so the string again settles at a fixed angle with the line perpendicular to the roof - correct.

Hence all four statements (A), (B), (C), (D) are correct.