A planet of mass $$M,$$ has two natural satellites with masses $${m_1}$$ and $${m_2}.$$ The radii of their circular orbits are $${R_1}$$ and $${R_2}$$ respectively, Ignore the gravitational force between the satellites. Define $${v_1},{L_1},{K_1}$$ and $${T_1}$$ to be , respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite $$1$$; and $${v_2},{L_2},{K_2},$$ and $${T_2}$$ to be the corresponding quantities of satellite $$2.$$ Given $${m_1}/{m_2} = 2$$ and $${R_1}/{R_2} = 1/4,$$ match the ratios in List-$${\rm I}$$ to the numbers in List-$${\rm II}.$$

LIST - I		LIST - II
P.	v1/v2	1.	1/8
Q.	L1/L2	2.	1
R.	K1/K2	3.	2
S.	T1/T2	4.	8

A rocket is launched normal to the surface of the Earth, away from the sun, along the line joining the Sun and the Earth. The Sun is $$3 \times 10{}^5$$ times heavier than the earth and is at a distance $$2.5 \times {10^4}$$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is $${V_c} = 11.2km\,{s^{ - 1}}.$$. The minimum initial velocity $$\left( {{v_s}} \right)$$ required for the rocket to be able to leave the sun-earth system is closest to (Ignore the the rotation and revoluation of the earth and the presence of any other planet) $${v_s} = 72km{s^{ - 1}}$$

A planet of radius R = $${1 \over {10}} \times $$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $${R \over 5}$$ on it and lower a wire of the same length and of linear mass density 10^-3 kg m^-1 into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 $$ \times $$ 10⁶ m and the acceleration due to gravity of Earth is 10 ms ^-2)

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is