# NCERT Physics Class 11 Exemplar Ch 8 Gravitation Part 5

## MCQ Type Questions

Q. 30 Show the nature of the following graph for a satellite orbiting the earth.

(a) KE vs orbital radius R

(b) PE vs orbital radius R

(c) TE vs orbital radius R.

Q.31 Shown are several curves (Fig.). Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

Answer: The trajectory of a particle under gravitational force of the earth will be a conic section (for motion outside the earth) with the centre of the earth as a focus. Only (c) meets this requirement.

Q.32 An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

Q.33 A mass m is placed at P a distance h along the normal through the centre O of a thin circular ring of mass M and radius r (Fig).

If the mass is removed further away such that OP becomes 2h, by what factor the force of gravitation will decrease, if h = r?

Answer: Only the horizontal component (i.e. along the line joining m and O) will survive. The horizontal component of the force on any point on the ring changes by a factor:

Q. 34 A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum l. As the radius r of the orbit increases, determine which of the above quantities increase and which ones decrease.

decreases.

decreases.

K decreases because v increases.

E increases because

L increases because

Q.35 Six-point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.