$A$ spherical hole of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$,as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is:

$A$ planet is orbiting the sun in an elliptical orbit. Let $U$ denote the potential energy and $K$ denote the kinetic energy of the planet at an arbitrary point on the orbit. Choose the correct statement.

How many times is the escape velocity $(V_e)$ of the orbital velocity $(V_0)$ for a satellite revolving near the Earth?

The radius and mass of the Earth are both increased by $0.5\%$. Which of the following statements is true at the surface of the 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 $A$ is $L$ and that of $B$ is $3L$,the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$: The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements,choose the most appropriate answer from the options given below: