$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

Two planets have masses $M$ and $16\, M$ and their radii are $a$ and $2\, a$ respectively. The separation between the centres of the planets is $10\, a.$ $A$ body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of the smaller planet,the minimum firing speed needed is

$A$ body of mass $m$ is released from a height of $2R$ above the Earth's surface. What will be its kinetic energy at a height of $R$ from the Earth's surface? (Where $R$ is the radius of the Earth)

$A$ body of mass $m$ is placed on the earth's surface. It is taken from the earth's surface to a height $h = 3R$ ($R$ is the radius of the earth). The change in gravitational potential energy of the body is

Two hypothetical planets of masses $m_1$ and $m_2$ are at rest when they are at an infinite distance apart. Because of the gravitational force,they move towards each other along the line joining their centres. What is their speed when their separation is $d$? (Speed of $m_1$ is $v_1$ and that of $m_2$ is $v_2$)

$A$ body of mass $m$ is taken from the Earth's surface to a height $h$ equal to twice the radius of the Earth $(h = 2R)$. The increase in potential energy will be ($g = \text{acceleration due to gravity on Earth's surface}$, $R = \text{radius of the Earth}$):