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
The total energy of a satellite in a circular orbit at a distance $(R+h)$ from the centre of the Earth varies as [ $R$ is the radius of the Earth and $h$ is the height of the oribit from Earth's surface]