Physics - NLM Question with Solution | TestHub

Take the gymnast (mass m) as the system; forces are his weight mg down and rope tension T up.

(A) Climbing at constant velocity means zero acceleration, so T = mg, not greater. Wrong.

(B) Hanging motionless: zero acceleration, so T = mg. Correct.

$$\mathrm{T}-\mathrm{mg}=\mathrm{ma}=0\Rightarrow \mathrm{T}=\mathrm{mg}$$

(C) Accelerating up the rope: net force upward, so T - mg = ma > 0, i.e. T > mg. Correct.

$$\mathrm{T}=\mathrm{m}(\mathrm{g}+\mathrm{a})>\mathrm{mg}$$

(D) Sliding down with downward acceleration: mg - T = ma > 0, i.e. T < mg. Correct.

$$\mathrm{T}=\mathrm{m}(\mathrm{g}-\mathrm{a})<\mathrm{mg}$$

Correct options: (B), (C), (D).