Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of their kinetic energies $$\left(K_B: K_A\right)$$ is :

An artillery piece of mass $$M_1$$ fires a shell of mass $$M_2$$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

A spherical body of mass $$100 \mathrm{~g}$$ is dropped from a height of $$10 \mathrm{~m}$$ from the ground. After hitting the ground, the body rebounds to a height of $$5 \mathrm{~m}$$. The impulse of force imparted by the ground to the body is given by : (given, $$\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$$)