A balloon carries a total load of 185 kg at normal pressure and temperature of $27^{\circ}\mathrm{C}$. 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 $-7^{\circ}\mathrm{C}$?

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Fluid Mechanics

A balloon carries a total load of 185 kg at normal pressure and temperature of

2 7^{\circ} 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^{\circ} C

(A)219.07 kg
(B)214.15 kg
(C)181.46 kg
(D)123.54 kg✓ Correct

Answer: (D)

Solution

The net lift equals the weight of displaced air minus the balloon-plus-gas weight; for ideal gases this scales with the air density

ρ \propto \frac{P}{T}

. Hence the carriable load scales as

\frac{P _{2}}{P _{1}} \cdot \frac{T _{1}}{T _{2}}

. With

P_{1} = 76 cm Hg, T_{1} = 300 K

and

P_{2} = 45 cm Hg, T_{2} = 266 K

185 \times \frac{45}{76} \times \frac{300}{266} \approx 123.5 kg

, option D.

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option

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