Question

A metal ball weighs 50 g in air and 25 g when dipped in a liquid of density $1.25~g/cm^{3}.$ The metal ball weighs _____ when dipped in a liquid of density $1.2~g/cm^{3}$

• A. 24 g
• B. 25 g
• C. 26 g
• D. 28 g

Hint:

Weight in liquid = Weight in air - (Volume $\times$ Density of Liquid).

Answer 1

The Correct Option is C

Step 1: Concept
Buoyant force ($F_B$) is equal to the weight of the displaced liquid: $F_B = V \cdot \rho_{liq} \cdot g$.

Step 2: Find Volume of Ball
In Liquid 1 ($\rho = 1.25$): Loss in weight = $50 - 25 = 25$ g.
$25 = V \times 1.25 \implies V = 20\text{ cm}^3$.

Step 3: Calculate Weight in Liquid 2
In Liquid 2 ($\rho = 1.2$): $F_B = 20 \times 1.2 = 24$ g.
Weight in liquid = Weight in air - $F_B = 50 - 24 = 26$ g.

Step 4: Conclusion
The ball weighs 26 g in the second liquid. Final Answer: (C)