In planetary motion the areal velocity of position vector of a planet depends on angular velocity ( ) and the distance of the planet from sun ( r ). If so, the correct relation for areal velocity is

in planetary motion the areal velocity of position vector

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $$\left( \omega \right)$$ and the distance of the planet from sun $$\left( r \right).$$ If so, the correct relation for areal velocity is

A. $$\frac{{dA}}{{dt}} \propto \omega r$$

B. $$\frac{{dA}}{{dt}} \propto {\omega ^2}r$$

C. $$\frac{{dA}}{{dt}} \propto \omega {r^2}$$

D. $$\frac{{dA}}{{dt}} \propto \sqrt {\omega r} $$

Answer : $$\frac{{dA}}{{dt}} \propto \omega {r^2}$$

Solution :
$$\frac{{dA}}{{dt}} = \frac{L}{{2m}} \Rightarrow \frac{{dA}}{{dt}} \propto vr \propto \omega {r^2}$$

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

View Answer

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

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $$\left( \omega \right)$$ and the distance of the planet from sun $$\left( r \right).$$ If so, the correct relation for areal velocity is

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

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $$\left( \omega \right)$$ and the distance of the planet from sun $$\left( r \right).$$ If so, the correct relation for areal velocity is

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

Practice More MCQ Question on Physics Section

Releted MCQ Question on
Basic Physics >> Gravitation

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Gravitation