Question

A stone of density \( 2000 \, \text{kg m}^{-3} \) completely immersed in a lake is allowed to sink from rest. If the effect of friction is neglected, then after 4 seconds, the stone will reach a depth of

• A. 78.4 m
• B. 39.2 m
• C. 19.6 m
• D. 9.8 m
• E. 24.6 m

Hint:

Inside a liquid, acceleration reduces due to buoyant force.

Answer 1

The Correct Option is C

Concept: Effective acceleration inside liquid: \[ a = g \left(1 - \frac{\rho_l}{\rho_s}\right) \]

Step 1: Given: \[ \rho_s = 2000, \quad \rho_l = 1000 \] \[ a = 10 \left(1 - \frac{1000}{2000}\right) = 10 \times \frac{1}{2} = 5 \]

Step 2: Use equation of motion: \[ s = \frac{1}{2} a t^2 \] \[ = \frac{1}{2} \times 5 \times 16 = 40 \text{ m} \] Correction: Using standard $g=9.8$: \[ a = 9.8 \times \frac{1}{2} = 4.9 \] \[ s = \frac{1}{2} \times 4.9 \times 16 = 39.2 \] Final Answer: \[ s = 39.2 \text{ m} \]