Motion of System of Particles and Rigid Body: NEET MCQ practice

Answer: C. on the line joining the particles.

For any two particles, regardless of their masses, the centre of mass always lies somewhere on the straight line connecting them. This is a fundamental definition, directly recalled from the chapter on centre of mass. Students who confuse this with a perpendicular bisector (which applies only for equal masses in symmetry) may be tempted by option A, but that's incorrect.

Answer: D. is equal to g

The center of mass of a system accelerates only due to external forces. Since gravity is the only external force on the two balls (neglecting air resistance), their combined center of mass accelerates downward with constant acceleration g, independent of their individual motions or masses. Options (a), (b), and (c) are incorrect because the acceleration remains g regardless of direction, masses, or speeds.

Answer: C. 1910.8 Nm

Power in rotational motion is given by P = τω, where ω is angular speed in rad/s. Here, ω = 30 × 2π ≈ 188.5 rad/s. Torque τ = P/ω = 360000/188.5 ≈ 1910.8 Nm. Option (b) looks tempting if you forget to multiply by 2π, and (a) & (d) are off by a factor of 10 or 100 from misplacing decimal places.

Answer: D. Direct proportionality

Torque relates to angular acceleration, not directly to angular displacement. There is no fixed proportionality or equality between them, so 'None of the mentioned' is correct. The wrong options (a) and (d) mistakenly suggest a simple inverse or direct proportionality, which does not hold in general rotational motion.

Answer: A. Torque

Torque is an axial vector because it arises from a cross product (position vector × force). Acceleration and force are polar vectors—they reverse direction under mirror reflection. This is a straightforward recall of a vector classification fact from rotational mechanics.