The potential energy for a force field $$\mathbf{F}$$ is given by $$u(x, y)=\cos (x+y)$$. The force acting on a particle at position given by co-ordinates $$(0, \pi / 6)$$ is

A machine gun fires 300 bullets per min if the mass of each bullet is 10 g and the velocity of the bullets is 600 ms^$$-$$1, the power (in kW) of the gun is

A force F = a + bx acts on a particle in the x-direction where a and b are constants. The work done by this force during a displacement from x = 0 to x = d is

The bob of a pendulum of length 2 m lies at P, when it reaches Q, it losses 10% of its total energy due to air resistance.

The velocity of bob at Q is

A ball of mass 0.5 kg is thrown up with initial speed 16 ms^$$-$$1 and reaches maximum height of 9 m. How much energy is dissipated by air drag acting on the ball during the ascent?

A time dependent force F = (8t) acts on a particle of mass 2 kg. If the particle starts from rest, the work done by the force during the first 1s will be

The work done by a force acting on a body is as shown in the following graph. The total work done in covering an initial distance of 40 m is