Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s^$$-$$1. Take 'g' constant with a value 10 m s^$$-$$2. The work done by the (i) gravitational force and the (ii) resistive force of air is

A particle moves from a point $$\left( { - 2\widehat i + 5\widehat j} \right)$$ to $$\left( {4\widehat j + 3\widehat k} \right)$$ when a force of $$\left( {4\widehat i + 3\widehat j} \right)$$ N is applied. How much work has been done by the force ?

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic enegy of the particle becomes equal to 8 $$ \times $$ 10^$$-$$4 J by the end of the second revoluation after the beginning of the motion ?