During an elastic collision between two bodies, which of the following statements are correct?
I. The initial kinetic energy is equal to the final kinetic energy of the system.
II. The linear momentum is conserved.
III. The kinetic energy during $\Delta \mathrm{t}$ (the collision time) is not conserved.
Three particles of mass $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed at the vertices A, B and C respectively of an equilateral triangle ABC of side 1 m . The centre of mass of the system from vertex A (located at origin) is
Two fly wheels are connected by a non-slipping belt as shown in the figure. $I_1=4 \mathrm{~kg} \mathrm{~m}^2, r_1=20 \mathrm{~cm}$, $\mathrm{I}_2=20 \mathrm{~kg} \mathrm{~m}^2$ and $\mathrm{r}_2=30 \mathrm{~cm}$. A torque of 10 Nm is applied on the smaller wheel. Then match the entries of column I with appropriate entries of column II.
I | Quantities | II | Their numerical Values (in SI units) |
(a) | Angular acceleration of smaller wheel | (i) | |
(b) | Torque on the larger wheel | (ii) | |
(c) | Angular acceleration of larger wheel | (iii) |

If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii, velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively, then