Mention the cause of an earthquake.

$A$ mass $m$,travelling at speed $V_0$ in a straight line from far away,is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$,the distance of closest approach between the mass and the black hole,is given by the relation:

$A$ spacecraft which is moving with a speed $u$ relative to the earth in the $x$-direction,enters the gravitational field of a much more massive planet which is moving with a speed $3u$ in the negative $x$-direction. The spacecraft exits following the trajectory as shown below. The speed of the spacecraft with respect to the earth a long time after it has escaped the planet's gravity is given by

$A$ satellite of mass $5M$ orbits the Earth in a circular orbit. At one point in its orbit,the satellite explodes into two pieces,one of mass $M$ and the other of mass $4M$. After the explosion,the mass $M$ ends up travelling in the same circular orbit,but in the opposite direction. After the explosion,the mass $4M$ is in:

What is the gravitational force exerted by the sphere of mass $M$ and radius $a$ on a ring of mass $m$ and radius $a$,where the distance between the center of the ring and the center of the sphere is $r = 1.73a = \sqrt{3}a$?

Weighing the Earth: You are given the following data: $g = 9.81 \; m/s^2$, $R_E = 6.37 \times 10^6 \; m$, the distance to the moon $R = 3.84 \times 10^8 \; m$, and the time period of the moon's revolution is $27.3$ days. Obtain the mass of the Earth $M_E$ in two different ways.