A body (mass $$\mathrm{m}$$ ) starts its motion from rest from a point distant $$R_0\left(R_0>R\right)$$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( $$\mathrm{G}=$$ universal constant of gravitation, $$\mathrm{M}=$$ mass of earth, $$\mathrm{R}$$ = radius of earth)

An ideal refrigerator has freezer at a temperature of $$-13^{\circ} \mathrm{C}$$. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is

1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

It is easier to spray water to which soap is added because addition of soap to water