NEET Physics Gravitation MCQs

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $\mathrm{R}_{\mathrm{E}}, \mathrm{~g}=$ acceleration due to gravity on the surface of earth) :

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at $R / 4$ depth under surface of earth?

Two planets $A$ and $B$ having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of $\mathrm{A}$ is ${L}$ and that of $B$ is $3 L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{G M_e m}{21 R_e}$. The value of $x$ is (take $\left.{R}_{{e}}=6370 \mathrm{~km}\right)$:

A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 \mathrm{R}$. If $\frac{10^4 \mathrm{R}}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius :

(use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{R}=$ radius of earth)

The mass of a planet is $\frac{1}{10}^{ext{th}}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ from the surface of the earth is: