what is the minimum energy required to launch a satellite

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R?$$

A. $$\frac{{5GmM}}{{6R}}$$

B. $$\frac{{2GmM}}{{3R}}$$

C. $$\frac{{GmM}}{{2R}}$$

D. $$\frac{{GmM}}{{3R}}$$

Answer : $$\frac{{5GmM}}{{6R}}$$

Solution :
Applying energy conservation
$$\eqalign{ & k + \left( { - \frac{{GMm}}{R}} \right) = \frac{1}{2}mv_0^2 + \left( { - \frac{{GMm}}{{R + h}}} \right) \cr & k - \frac{{GMm}}{R} = \frac{1}{2}m + \left( {\frac{{Gm}}{{R + 2R}}} \right) - \frac{{GMm}}{{R + 2R}} \cr & \therefore k = \frac{{5GMm}}{{6R}} \cr} $$

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

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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. $$\frac{1}{4}mgR$$

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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. $$730$$

View Answer

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. $$4 \,hr$$

View Answer

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R?$$

Releted MCQ Question on
Basic Physics >> Gravitation

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-

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-

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 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-

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Gravitation

Practice More MCQ Question on Physics Section

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R?$$

Releted MCQ Question on Basic Physics >> Gravitation

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-

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-

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 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-

Practice More Releted MCQ Question on Gravitation

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Releted MCQ Question on
Basic Physics >> Gravitation

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Gravitation