Question

A spring balance measures the weight of an object in air to be $0.1N$. It shows a reading of $0.08N$ when the object is completely immersed in water. If the value of acceleration due to gravity is $10m/s^2$, the volume of the object is

• A. $20{cm}^3$
• B. $80{cm}^3$
• C. $200{cm}^3$
• D. $2{cm}^3$

Answer 1

Answer: (D)

$2{cm}^3$

Given,

Weight of the object in air $=0.1N$

Weight of the object in water $=0.08N$

The volume of the object $\left(V\right)=?$

The reduction in weight is due to buoyant force $\left(F_B\right)$.

$\therefore$ Buoyant force $(0.1-0.08)=0.02N$

From Archemede's principle,

$F_B=\text{Weight of the displaced water}$ $=\text{Volume of water displaced}\times \text{Density of water}\times g$

$\Rightarrow 0.02=V\times {10}^3\times 10$

$\Rightarrow V=\frac{0.02}{{10}^4}{m}^3=0.02\times \frac{{10}^6}{{10}^4}{cm}^3=2{cm}^3$