In planetary motion the areal velocity of position vector of a planet depends on angular velocity $(\omega )$ 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 of a planet depends on angular velocity $(\omega )$ and the distance of the planet from sun $(r)$. 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} $
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A planet is moving in an elliptical orbit around the sun. If $T, V, E$ and $L$ stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ?
A planet is moving in an elliptical orbit around the sun. If $T, V, E$ and $L$ stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ?
- [AIPMT 1990]
The maximum and minimum distances of a comet from the sun are $8 \times {10^{12}}\,m$ and $1.6 \times {10^{12}}\,m$. If its velocity when nearest to the sun is $60\, m/s$, what will be its velocity in $m/s$ when it is farthest
The maximum and minimum distances of a comet from the sun are $8 \times {10^{12}}\,m$ and $1.6 \times {10^{12}}\,m$. If its velocity when nearest to the sun is $60\, m/s$, what will be its velocity in $m/s$ when it is farthest
Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$ : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below:
Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$ : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below:
- [JEE MAIN 2024]
A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon’s orbit. The satellite completes one revolution in
A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon’s orbit. The satellite completes one revolution in