A particle moves in a conservative force field where its potential energy U is given by U(x) = ax^2 - bx. The particle will be in stable equilibrium at position x equal to: MCQ with Answer and Explanation

Explanation:
7.50 has three significant figures (7,5,0). Trailing zero after decimal is significant. If it were 7.5 cm, two significant figures. Precision indicated by decimal places.

Explanation:
R = 2f = 40 cm. For convex, f positive, R positive.

Explanation:
The effective acceleration due to gravity at latitude lambda is g' = g - R * w^2 * cos^2(lambda), where w is angular velocity. At the equator, lambda = 0, so cos(0) = 1. This subtracts the maximum outward centrifugal acceleration (Rw^2) from g. At the poles, lambda = 90, centrifugal effect is zero. Thus, g is minimum exactly at the equator.