91Ó°ÊÓ

Two small drops of mercury, each of radius \(R\), coalesce to form a single large drop. The ratio of the total surface energies before and after the change is (a) \(1: 2^{1 / 3}\) (b) \(2^{1 / 3}: 1\) (c) \(2: 1\) (d) \(1: 2\)

Radius of a soap bubble is increased from \(R\) to \(2 R\) work done in this process in terms of surface tension is [CPMT 1991; RPET 2001; BHU 2003] (a) \(24 \pi R^{2} S\) (b) \(48 \pi R^{2} S\) (c) \(12 \pi R^{2} S\) (d) \(36 \pi R^{2} S\)

The work done in blowing a soap bubble of \(10 \mathrm{~cm}\) radius is (surface tension of the soap solution is \(\left.\frac{3}{100} N / m\right)\) [MP PMT 1995; MH CET 2002] (a) \(75.36 \times 10^{-4} J\) (b) \(37.68 \times 10^{-4} J\) (c) \(150.72 \times 10^{-4} J\) (d) \(75.36 J\)

The radii of two soap bubbles are \(R_{1}\) and \(R_{2}\) respectively. The ratio of masses of air in them will be (a) \(\frac{R_{1}^{3}}{R_{2}^{3}}\) (b) \(\frac{R_{2}^{3}}{R_{1}^{3}}\) (c) \(\left(\frac{P+\frac{4 T}{R_{1}}}{P+\frac{4 T}{R_{2}}}\right) \frac{R_{1}^{3}}{R_{2}^{3}}\) (d) \(\left(\frac{P+\frac{4 T}{R_{2}}}{P+\frac{4 T}{R_{1}}}\right) \frac{R_{2}^{3}}{R_{1}^{3}}\)

On dipping one end of a capillary in liquid and inclining the capillary at an angles \(30^{\circ}\) and \(60^{\circ}\) with the vertical, the lengths of liquid columns in it are found to be \(l_{1}\) and \(l_{2}\) respectively. The ratio of \(l_{1}\) and \(l_{2}\) is (a) \(1: \sqrt{3}\) (b) \(1: \sqrt{2}\) (c) \(\sqrt{2}: 1\) (d) \(\sqrt{3}: 1\)