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 goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time?

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).

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:

For a satellite to orbit around the earth,which of the following must be true?

How many times is the escape velocity $(V_e)$ of the orbital velocity $(V_0)$ for a satellite revolving near the Earth?

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?