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?

$A$ satellite is revolving in a circular orbit at a height $h$ from the Earth's surface,such that $h \ll R$,where $R$ is the radius of the Earth. Assuming that the effect of the Earth's atmosphere can be neglected,the minimum increase in the speed required so that the satellite could escape from the gravitational field of the Earth is:

$A$ 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:

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:

Two bodies of masses $m_1$ and $m_2$ initially at rest at infinite distance apart move towards each other under gravitational force of attraction. Their relative velocity of approach when they are separated by a distance $r$ is ($G=$ universal gravitational constant.)

$A$ gas molecule of mass $M$ at the surface of the Earth has kinetic energy equivalent to $0\,^{\circ}C$. If it were to go up straight without colliding with any other molecules,how high would it rise? Assume that the height attained is much less than the radius of the Earth. ($k_B$ is Boltzmann constant)