JEE MAIN - Physics (2021 - 25th July Evening Shift - No. 11)
Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :
$${{{r_1}{r_2}} \over {{r_1} + {r_2}}}$$
$$\sqrt {{r_1}{r_2}} $$
$$\sqrt {r_1^2 + r_2^2} $$
$${{{r_1} + {r_2}} \over 2}$$
Explanation
_25th_July_Evening_Shift_en_11_2.png)
no. of moles is conserved
n1 + n2 = n3
P1V1 + P2V2 = P3V
$${{4S} \over {{r_1}}}\left( {{4 \over 3}\pi r_1^3} \right) + {{4S} \over {{r_2}}}\left( {{4 \over 3}\pi r_2^3} \right) = {{4S} \over {{r_3}}}\left( {{4 \over 3}\pi r_3^3} \right)$$
$$r_1^2 + r_2^2 = r_3^2$$
$${r_3} = \sqrt {r_1^2 + r_2^2} $$
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