One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

A solid sphere of radius R and density $$\rho $$ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3$$\rho $$. The complete arrangement is placed in a liquid of density 2$$\rho $$ and is allowed to reach equilibrium. The correct statement(s) is (are)

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $$C.$$ The switch $${S_1}$$ is pressed first to fully charge the capacitor $${C_1}$$ and then released. The switch $${S_2}$$ is then pressed to charge the capacitor $${C_2}.$$ After some time, $${S_2}$$ is released and then $${S_3}$$ is pressed. After some time