Question

A stone weighs 90 N in air and when immersed in water it weighs 50 N. specific gravity of stone is:
1. 0.556
2. 0.444
3. 1.8
4. 2.25
5.

Answer 1

Correct Answer - Option 4 : 2.25

Concept:

The original weight of the stone is given by mg

W = ρb V g

When kept in a fluid, the apparent weight is given by

Wa = W – Fb = ρbV g – ρf V g = (ρb – ρv)V g 

Calculation:

Given

Weight in air = 90 N

⇒ (ρb – ρa)V g = 90      ---(1)

Weight in water = 50 N

⇒ (ρb – ρW)V g = 50       ---(2)

From equation 1 and 2,

\(\frac{{{\rho _b} - {\rho _a}}}{{{\rho _b} - {\rho _w}}} = \frac{{900}}{{50}}\)

We have ρa = 1.18 kg/m3, ρw = 1000 kg/m3,

\(\Rightarrow \frac{{{\rho _b} - 1.18}}{{{\rho _b} - 1000}} = \frac{{90}}{{50}} \Rightarrow {\rho _b} = 2248.525\;kg/{m^3}\)

Specific gravity of the stone = 2248.525/1000 = 2.248 kg/m3 ≈ 2.25 kg/m3