Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms^$$-$$2].

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms^$$-$$1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?

[Specific heat capacity of iron = 0.42 Jg^$$-$$1 $$^\circ$$C^$$-$$1]