Question:
If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the center of the Sun, its areal velocity is :
If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the center of the Sun, its areal velocity is :
Updated On: Oct 10, 2024
- $\frac{4 L}{m}$
- $\frac{L}{m}$
- $\frac{ L}{ 2 m}$
- $\frac{2L}{m}$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$ \frac{dA}{dt} = \frac{L}{2m}$
Was this answer helpful?
0
0
Top Questions on Gravitation
- A body of mass $ 1.5 \, \text{kg} $ is dropped from a height of $ 20 \, \text{m} $. What is its speed just before hitting the ground? (Assume $ g = 9.8 \, \text{m/s}^2 $)
- MHT CET - 2025
- Physics
- Gravitation
- What is the gravitational force between two objects of masses \( m_1 = 10 \, \text{kg} \) and \( m_2 = 20 \, \text{kg} \), separated by a distance of \( r = 5 \, \text{m} \)? (Gravitational constant \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
- MHT CET - 2025
- Physics
- Gravitation
- The value of \( g \) at height \( h \) above Earth's surface is \( \frac{g}{\sqrt{3}} \). Find \( h \) in terms of the radius of the Earth.
- MHT CET - 2025
- Physics
- Gravitation
- At a height \( h \) above the Earth's surface, the acceleration due to gravity becomes \( \frac{g}{\sqrt{3}} \). What is the value of \( h \) in terms of the Earth's radius \( R \)?
- MHT CET - 2025
- Physics
- Gravitation
- If \( r_1, v_1, L_1 \) and \( r_2, v_2, L_2 \) are radii, velocities, and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively, then
- KCET - 2025
- Physics
- Gravitation
View More Questions
Questions Asked in JEE Main exam
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Trigonometry
- The spin-only magnetic moment (\(\mu\)) value (B.M.) of the compound with the strongest oxidising power among \(Mn_2O_3\), \(TiO\), and \(VO\) is ________________________ B.M. (Nearest integer).
- JEE Main - 2025
- Magnetic moment
- Atomic number of element with lowest first ionisation enthalpy is:
- JEE Main - 2025
- Periodic Table
- Let \( z_1, z_2, z_3 \) be three complex numbers on the circle \( |z| = 1 \) with \( \arg(z_1) = -\frac{\pi}{4}, \arg(z_2) = 0 \) and \( \arg(z_3) = \frac{\pi}{4} \). If \( |z_1 \overline{z_2} + z_2 \overline{z_3} + z_3 \overline{z_1}|^2 = \alpha + \beta \sqrt{2} \), where \( \alpha, \beta \in \mathbb{Z} \), then the value of \( \alpha^2 + \beta^2 \) is :
- JEE Main - 2025
- complex numbers
- The kinetic energy of translation of the molecules in 50 g of CO\(_2\) gas at 17°C is:
- JEE Main - 2025
- The Kinetic Theory of Gases
View More Questions
Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].