Question

A balloon filled with hydrogen has a volume of $1m^3$ and its mass is $1kg$. The volume of the block of a very light material which it can just lift is:
[Density of material of block is $91.3kg/m^3$ and that of air is $1.3kg/m^3$]

• A. $\frac{1}{300}{m}^3$
• B. $\frac{1}{400}{m}^3$
• C. $\frac{1}{500}{m}^3$
• D. $\frac{1}{600}{m}^3$

Answer 1

The correct option is A $\frac{1}{300}{m}^3$

density of block $=91.3kg/m^3$
uplift from air $=1.3kg\times g$
Downforce from balloon $=1kg\times g$
So,
Extra weight that can be lifted $=0.30gN$
So, Considering buoyant force on itself,
$\Rightarrow 0.30g+1.3vg=91.3vg$ [where $V$ is Volume of the block]
$\Rightarrow 0.3=90V$
$\Rightarrow V=\frac{1}{300}{m}^3$