JEE MAIN - Physics (2021 - 27th August Morning Shift - No. 5)
A balloon carries a total load of 185 kg at normal pressure and temperature of 27$$^\circ$$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. Assuming the volume constant?
181.46 kg
214.15 kg
219.07 kg
123.54 kg
Explanation
Pm = $$\rho$$RT
$$\therefore$$ $${{{P_1}} \over {{P_2}}} = {{{\rho _1}{T_1}} \over {{\rho _1}{T_2}}}$$
$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{P_1}{T_2}} \over {{P_2}{T_1}}} = \left( {{{76} \over {45}}} \right) \times {{266} \over {300}}$$
$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{M_1}} \over {{M_2}}} = {{76 \times 266} \over {45 \times 300}}$$
$$\therefore$$ $${M_2} \Rightarrow {{45 \times 300 \times 185} \over {76 \times 266}} = 123.54$$ kg
$$\therefore$$ $${{{P_1}} \over {{P_2}}} = {{{\rho _1}{T_1}} \over {{\rho _1}{T_2}}}$$
$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{P_1}{T_2}} \over {{P_2}{T_1}}} = \left( {{{76} \over {45}}} \right) \times {{266} \over {300}}$$
$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{M_1}} \over {{M_2}}} = {{76 \times 266} \over {45 \times 300}}$$
$$\therefore$$ $${M_2} \Rightarrow {{45 \times 300 \times 185} \over {76 \times 266}} = 123.54$$ kg
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