The work done in blowing a soap bubble of radius $$\mathrm{R}$$ is '$$\mathrm{W}_1$$' at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius $$2 \mathrm{R}$$ is blown and the work done is '$$\mathrm{W}_2$$'. Then

A capacitor of capacitance $$50 \mu \mathrm{F}$$ is connected to a.c. source $$\mathrm{e}=220 \sin 50 \mathrm{t}$$ ($$\mathrm{e}$$ in volt, $$\mathrm{t}$$ in second). The value of peak current is

Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is

The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\mathrm{d}$$ apart. What should be the minimum speed with which a body of mass '$$m$$' should be projected from a point midway between their centres, so as to escape to infinity?