Column-I Column-II (P) In the situation shown, the gravitational potential energy is minimum. (Q) On small appropriate displacement, body can execute SHM. (R) For body to execute SHM, amplitude should not be larger than limiting value. (S) If the mass of body increases without changing its size, its time period of oscillation can change (T) If the size of body increases without increasing mass, its time period of oscillation can change.

Engineering

Physics

Equilibrium

Basics of Simple Harmonic Motion

Buoyancy

Question

Column-I	Column-II
	(P) In the situation shown, the gravitational potential energy is minimum.
	(Q) On small appropriate displacement, body can execute SHM.
	(R) For body to execute SHM, amplitude should not be larger than limiting value.
	(S) If the mass of body increases without changing its size, its time period of oscillation can change
	(T) If the size of body increases without increasing mass, its time period of oscillation can change.

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Aℓ₀g × ρ_w = mg
mg – A (ρ₀ + x) g ρ_w = ma_n
   a_n = $\frac{- {Aρ}_{w} gx}{m}$
   $ω = \sqrt{\frac{{Aρ}_{w} gx}{m}}$ = $\sqrt{\frac{ρ_{w} g}{ρ_{w} l}}$
(C)   $T = 2 π \sqrt{\frac{I}{mgx}}$ = $T = 2 π \sqrt{\frac{I}{mgx}}$ = $2 n \sqrt{\frac{R}{2 g}}$