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?

A straight rod length $$L(t),$$ hinged at one end freely extensible at the other end, roates through an angle $$\theta \left( t \right)$$ about the hinge. At time $$t,$$ $$L(t)=1m,$$ $$L(t)=1m/s,$$ $$\theta \left( t \right) = \pi /4$$ rad and $$\mathop \theta \limits^ \cdot \left( t \right) = 1\,\,rad/s.$$ The magnitude of the velocity at the other end of the rod is