A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity $$V$. The velocity at the point of contact between the object and the floor is

The coefficient of restitution of a perfectly plastic impact is

A stone with mass of $$0.1$$kg is catapulted as shown in the figure. The total force $${F_x}$$ (in N) exerted by the rubber band as a function of distance $$x$$ (in m) is given by $${F_x} = 300{x^2}.$$ If the stone is displayed by $$0.1$$ m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber bad is

A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is $$\mu = 0.2.$$ A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 $$N$$. What will be the tension, $$T$$ (inN) in the cable if the man is just able to move the block to the right?