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NCERT Exemplar · Q3

Q.A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is

(a) constant and equal to mgmg in magnitude.
(b) constant and greater than mgmg in magnitude.
(c) variable but always greater than mgmg.
(d) at first greater than mgmg, and later becomes equal to mgmg.
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The ground reaction force must first exceed mgmg to accelerate the man upward from rest, then return to mgmg once he moves at constant speed (or stops). The correct option is (D).

The key is to think about Newton’s second law — not just the third law. When the man squats and then stands up, his centre of mass does not move at constant velocity. It starts at rest, accelerates upward, then decelerates to rest again at the top. The ground reaction force is the upward normal force NN from the floor. The man’s weight mgmg acts downward. The net force on the man is N−mgN - mg, and this equals mama, where aa is the acceleration of his centre of mass.

If the man simply stood still, N=mgN = mg. But during the act of standing, his centre of mass must gain upward speed, so there must be a period of upward acceleration. That requires N>mgN > mg. Later, as he approaches the upright position, he must slow down (decelerate upward), which means N<mgN < mg briefly. However, the question’s options only mention “greater than mgmg” and “equal to mgmg”, so the simplest correct description is that NN is first greater than mgmg, then becomes equal to mgmg once he is stationary.

Let’s walk through the phases.

  1. Initial state (squatting, at rest)

    The man is stationary on the ground. His centre of mass has zero velocity. The net force is zero, so N=mgN = mg. But this is only the starting point — the process hasn’t begun yet.

  2. Beginning to stand — upward acceleration

    To start moving upward, the man must push harder against the ground. By Newton’s third law, the ground pushes back with an equal and opposite force. So NN becomes greater than mgmg. The net upward force N−mgN - mg provides the upward acceleration aa.

N−mg=ma⇒N=m(g+a)>mgN - mg = ma \quad \Rightarrow \quad N = m(g + a) > mg

  1. Middle of the motion — possible constant speed

    If the man rises at constant speed for a while, then a=0a = 0 and N=mgN = mg during that interval. But in a natural squat-to-stand movement, the acceleration phase is short and followed by deceleration. The question’s options don’t mention a period where N<mgN < mg, so the simplest match is that after the initial acceleration, NN returns to mgmg as the man becomes stationary.

  2. Nearing the top — deceleration

    To stop at the upright position, the man must have a downward acceleration (i.e., upward deceleration). That would require N<mgN < mg. However, the options given do not include “less than mgmg” at any stage. So the intended answer focuses on the fact that NN is first greater than mgmg (to start the motion) and later equal to mgmg (when at rest or moving at constant speed).

Watch out

A common mistake is to think that because the man is “pushing” on the ground, the reaction is always greater than mgmg. But once he is moving at constant speed or is stationary, the net force is zero, so N=mgN = mg. The extra force is only needed to change his speed.

Tip

Think of standing up as a controlled upward throw of your own body. To throw something upward, you must exert a force greater than its weight initially. Once it’s moving, you can ease off.

Thus, the reaction force is not constant — it varies — and it is greater than mgmg only during the upward acceleration phase, then equal to mgmg when the man is at rest (or moving uniformly).

✓Final answer

The correct option is (D): at first greater than mgmg, and later becomes equal to mgmg.

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