A particle is projected vertically upwards with a speed $u$ from the surface of the Earth. If the air resistance is proportional to the square of the velocity ($F = -kv^2$), what is the maximum height reached by the particle? (Assume $g$ is constant and $m$ is the mass of the particle)

A gun fires bullet each of mass 1 g with velocity of $10\;{\rm{m}}{{\rm{s}}^{ - 1}}$ by exerting a constant force of 5 g weight. Then the number of bullets fired per second is (Take $g = 10\;{\rm{m}}{{\rm{s}}^{ - 2}})$

Two identical balls are held at different heights above the ground. The ball held at the greater height has:

The work done against gravity in taking 10 kg mass at 1m height in 1 sec will be

A particle is subjected to a force $F = -kx + \frac{a}{x^3}$, where $k$ and $a$ are positive constants. What is the equilibrium position of the particle?

The potential energy of a particle in a force field is $U = \frac{A}{{{r^2}}} - \frac{B}{r}$, where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

If the mass of an object is doubled while keeping its height constant, its gravitational potential energy will:

A machine gun mounted on a 2000 kg car on a horizontal frictionless surface fires 10 bullets per second. If 10 g be the mass of each bullet and 500 ${\rm{m}}{{\rm{s}}^{ - 1}}$, the velocity of each bullet, then the acceleration of the car will be

A man, by working a hand pump fixed to a well, pumps out $10{\rm{\;}}{{\rm{m}}^3}$ water in 1 s. If the water in the well is 10 m below the ground level, then the work done by the man is $\left( {{\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}} \right)$

A rope ladder with a length $l$ carrying a man with a mass m at its end is attached to the basket of balloon with a mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. Then the potential energy of the man

An iron nail is dropped from a height h from the level of a sand bed. If it penetrates through a distance x in the sand before coming to rest, then average force exerted by the sand on nail is