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?

A monoatomic gas $$\left(\gamma=\frac{5}{3}\right)$$ initially at $$27^{\circ} \mathrm{C}$$ having volume '$$\mathrm{V}$$' is suddenly compressed to one-eighth of its original volume $$\left(\frac{\mathrm{V}}{8}\right)$$. After the compression its temperature becomes

Two parallel conducting wires of equal length are placed distance 'd' apart, carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

Self inductance of a solenoid cannot be increased by