Question

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

A. $$2$$
B. $$\frac{1}{2}$$  
C. $$\frac{1}{{\sqrt 2 }}$$
D. $$\sqrt 2 $$
Answer :   $$\frac{1}{2}$$
Solution :
Potential energy, $$U = - \frac{{G{M_e}m}}{{{R_e}}}$$
where,
$${M_e} =$$  mass of the earth
$$m =$$  mass of satellite
$${R_e} =$$  radius of the earth
$$G =$$  gravitational constant
or $$\,\left| U \right| = \frac{{G{M_e}m}}{{{R_e}}}$$
Kinetic energy, $$K = \frac{1}{2}\frac{{G{M_e}m}}{{{R_e}}}$$
Thus, $$\frac{K}{{\left| U \right|}} = \frac{1}{2}\frac{{G{M_e}m}}{{{R_e}}} \times \frac{{{R_e}}}{{G{M_e}m}} = \frac{1}{2}$$
NOTE
The total energy, $$E = K + U = - \frac{{G{M_e}m}}{{2r}}$$
Gravitation mcq solution image
This energy is constant and negative, i.e. the system is closed. To farther the satellite from the earth, the greater is its total energy.

Releted MCQ Question on
Basic Physics >> Gravitation

Releted Question 1

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

A. Decrease
B. Remain unchanged
C. Increase
D. Be zero
Releted Question 2

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

A. $$\frac{1}{2}\,mgR$$
B. $$2\,mgR$$
C. $$mgR$$
D. $$\frac{1}{4}mgR$$
Releted Question 3

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A. $$64.5$$
B. $$129$$
C. $$182.5$$
D. $$730$$
Releted Question 4

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$   Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$    will approximately be-

A. $$\frac{1}{2}\,hr$$
B. $$1 \,hr$$
C. $$2 \,hr$$
D. $$4 \,hr$$

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Gravitation


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