Q31 of 38 Page 62

Shown are several curves (Fig. 8.2). Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

(a)


(b)


(c)


(d)


(e)


(f)


The trajectory traced by a projectile under the action of gravitational force will always be a conic section. When the distance thrown is small compared to the radius of the earth then the projectile follows a parabolic trajectory as demonstrated by the so - called projectile motion in the analysis of newton’s equations of motion. However, when the distance is comparable to the earth’s radius the trajectory is an ellipse according to Kepler’s laws. Therefore, the correct trajectory is (c)


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29

Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.

 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.


 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?

 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. 8.3).


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