Question:
If $G$ is the universal gravitational constant and $p$ is the uniform density of a planet. Then shortest possible period of rotation of the planet can be
If $G$ is the universal gravitational constant and $p$ is the uniform density of a planet. Then shortest possible period of rotation of the planet can be
Updated On: Mar 6, 2024
- $\sqrt{\frac{\pi\,G}{2\rho}}$
- $\sqrt{\frac{3\pi\,G}{\rho}}$
- $\sqrt{\frac{\pi}{6G\rho}}$
- $\sqrt{\frac{3\pi}{G\rho}}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Answer (d) $\sqrt{\frac{3\pi}{G\rho}}$
Was this answer helpful?
0
1
Top Questions on Gravitation
- An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight, corrected to the nearest integer is ($R_E$ is the radius of the earth):
- NEET (UG) - 2024
- Physics
- Gravitation
- The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:
- NEET (UG) - 2024
- Physics
- Gravitation
- A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:
- JEE Main - 2024
- Physics
- Gravitation
- A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the force of attraction between the planet and the star is proportional to $R^{-\frac{3}{2}}$, then choose the correct option:
- JEE Main - 2024
- Physics
- Gravitation
- Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?
- JEE Main - 2024
- Physics
- Gravitation
View More Questions
Questions Asked in COMEDK UGET exam
- A $2\,kg$ mass lying on a table is displaced in the horizontal direction through $50\,cm$. The work done by the normal reaction will be
- COMEDK UGET - 2015
- work, energy and power
- The numbers of $ {H^+}$ ions present in 1 mL of a solution whose pH is 13
- COMEDK UGET - 2015
- Equilibrium
- A mixture of methylamine and dimethylamine is given to you. The reagents used to separate the components of the mixture are
- $\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
- COMEDK UGET - 2015
- Inverse Trigonometric Functions
- Pick the incorrect statement among those given below.
- COMEDK UGET - 2015
- Chemical bonding and molecular structure
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].