Sand is being dropped from a stationary dropper at a rate of $$0.5 \,\mathrm{kgs}^{-1}$$ on a conveyor belt moving with a velocity of $$5 \mathrm{~ms}^{-1}$$. The power needed to keep the belt moving with the same velocity will be :

As per the given figure, two blocks each of mass $$250 \mathrm{~g}$$ are connected to a spring of spring constant $$2 \,\mathrm{Nm}^{-1}$$. If both are given velocity $$v$$ in opposite directions, then maximum elongation of the spring is :

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms^$$-$$1 gets embedded in it, then loss of kinetic energy will be :

A body of mass $$0.5 \mathrm{~kg}$$ travels on straight line path with velocity $$v=\left(3 x^{2}+4\right) \mathrm{m} / \mathrm{s}$$. The net workdone by the force during its displacement from $$x=0$$ to $$x=2 \mathrm{~m}$$ is :