Question

The volume of a balloon filled with hydrogen gas which will be sufficient to lift a load of 25 kg. Given the densities of air and hydrogen are $12.9\times {10}^{-4}$ grams per centimetre cube and $9\times {10}^{-5}$ gram per centimetre cube.

• A. 25 m cube
• B. 24 metre cube
• C. 20.83 M cube
• D. None of these

Answer 1

The correct option is C 20.83 M cube

Given: Mass of the load($m_{l}g$) = 25 kg, density of air(${\rho }_a$) $12.9\times {10}^{-4}gm/c{m}^3$ and density of hydrogen(${\rho }_h$) is $9\times {10}^{-5}gm/c{m}^3$

Solution:

Gravitational force will act on both balloon and load in downward direction and buoyancy will act on the balloon in upward direction. To lift the load ,

${\rho }_{a}Vg\ge {\rho }_{h}Vg+m_{l}g$

For just sufficient condition,

${\rho }_{a}Vg={\rho }_{h}Vg+m_{l}g$

$\Rightarrow (12.9\times {10}^{-4}-9\times {10}^{-5})V=25\times {10}^3$

$\Rightarrow V=2.08\times {10}^{7}cc$

$\therefore ,V=20.83m^3$

Hence correct answer is C.