If the mass of the Earth remains constant and its radius is reduced to $\frac{1}{n}$ of its original value,what will be the duration of $1$ day?

When a satellite in a circular orbit around the earth enters the atmospheric region,it encounters small air resistance to its motion. Then

Statement $(A)$ Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement $(B)$ The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement $(C)$ The escape velocity of a body is independent of the altitude of the point of projection.

Suppose the acceleration due to gravity at the earth's surface is $10 \, m/s^2$ and at the surface of Mars it is $4.0 \, m/s^2$. $A$ $60 \, kg$ passenger travels from the Earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which curve in the figure best represents the weight (net gravitational force) of the passenger as a function of time?

$A$ solid sphere of uniform density and radius $4$ units is located with its centre at the origin $O$ of coordinates. Two spheres of equal radii $1$ unit with their centres at $A(-2, 0, 0)$ and $B(2, 0, 0)$ respectively are taken out of the solid leaving behind spherical cavities as shown in the figure.

Two particles of equal mass $m$ move in a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their center of mass is