Q68 / 90 · JEE Main 2021 (27 Aug Shift 1) · Physics

A balloon carries a total load of $185 kg$ at normal pressure and temperature of $27 ° C .$ What load will the balloon carry on rising to a height at which the barometric pressure is $45 cm$ of $Hg$ and the temperature is $- 7 ° C .$ Assuming the volume constant?

Solution

$ρ_{air} = g v = m g$

$ρ_{air} = V = 185 kg$

$ρ_{air} g v = m' g$

$ρ_{a i r} (\frac{P^{'}}{P} \times \frac{T}{T^{'}}) V = m^{'}$

$185 [\frac{45}{76} \times \frac{300}{266}] = m^{'}$

$m ’ = 123.54 kg$

Hence, the correct answer is option: 'B'.