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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Fluids

BITSAT 2020 · Physics · Mechanical Properties of Fluids

A body of density ^ is dropped from rest at a height h into a lake...

A body of density ρ′\rho^{\prime} is dropped from rest at a height h into a lake of density ρ\rho where ρ>ρ′\rho > \rho^{\prime} neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:A body of density ^ is dropped from rest at a height h into a lake of density where > ^ neglecting all dissipative

Options

  1. Ahρ−ρ′\frac{\mathrm{h}}{\rho-\rho^{\prime}}
  2. Bhρ′ρ\frac{\mathrm{h} \rho^{\prime}}{\rho}
  3. Chρ′ρ−ρ′\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}
  4. Dhρρ−ρ′\frac{h \rho}{\rho-\rho^{\prime}}

Correct answer

C. hρ′ρ−ρ′\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}

Step-by-step solution

The effective acceleration of the body \mathrmg′=(1−ρρ′)g\mathrmg^{\prime}=\left(1-\frac{\rho}{\rho^{\prime}}\right) \mathrm{g} A body of density ^ is dropped from rest at a height h into a lake of density where > ^ neglecting all dissipative
Now, the depth to which the body sinks \mathrmh′=(\mathrmu22g′)=2gh2g′=gh\mathrmg′=h×ρ′ρ−ρ′\mathrmh^{\prime}=\left(\frac{\mathrmu^{2}}{2 \mathrm{ g}^{\prime}}\right)=\frac{2 \mathrm{gh}}{2 \mathrm{ g}^{\prime}}=\frac{\mathrm{gh}}{\mathrmg^{\prime}}=\frac{\mathrm{h} \times \rho^{\prime}}{\rho-\rho^{\prime}}
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