A cylindrical block of mass M and area of cross section A is floating in a liquid of density and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________. [2026]

Question

A cylindrical block of mass M and area of cross section A is floating in a liquid of density $ρ$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________. [2026]

Smart Achievers · Accepted Answer

(4)

$At equilibrium$

$ρ A h g = M g$

$After displacing by x,$

$M a = - ρ A (h + x) g + M g$

$M a = - ρ A h g - ρ A x g + M g$

$M a = - ρ A x g$

$a = (\frac{- ρ A g}{M}) x$

$on comparing with,$

$a = - ω^{2} x$

$ω = \sqrt{\frac{ρ A g}{M}}$

$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{M}{ρ A g}}$

Solution

Q.
A cylindrical block of mass M and area of cross section A is floating in a liquid of density $ρ$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________. [2026]

1 $π \sqrt{\frac{ρ A}{M g}}$

2 $2 π \sqrt{\frac{ρ A}{M g}}$

3 $π \sqrt{\frac{2 M}{ρ A g}}$

4 $2 π \sqrt{\frac{M}{ρ A g}}$

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Solution

Q. A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________. [2026]

1 πρAMg

2 2πρAMg

3 π2MρAg

4 2πMρAg