If a tunnel is cut at any orientation through the Earth,a ball released from one end will reach the other end in time ........ $\text{min}$ (neglect Earth's rotation).

Mention the cause of an earthquake.

$A$ spherically symmetric gravitational system of particles has a mass density $\rho = \begin{cases} \rho_0 & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$ where $\rho_0$ is a constant. $A$ test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r$ $(0 < r < \infty)$ from the centre of the system is represented by:

Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same direction because of their mutual gravitational attractive force. The velocity of a particle is given by

Every planet revolves around the sun in an elliptical orbit. Which of the following statements are correct?
$A.$ The force acting on a planet is inversely proportional to the square of the distance from the sun.
$B.$ The force acting on the planet is inversely proportional to the product of the masses of the planet and the sun.
$C.$ The centripetal force acting on the planet is directed away from the sun.
$D.$ The square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
Choose the correct answer from the options given below:

Three identical spheres of mass $m$ are placed at the vertices of an equilateral triangle of side length $a$. When released,they interact only through gravitational force and collide after a time $T = 4 \text{ s}$. If the sides of the triangle are increased to length $2a$ and the masses of the spheres are made $2m$,then they will collide after . . . . . . seconds.