Question:
Average density of the earth :
Average density of the earth :
Updated On: Apr 7, 2024
- does not depend on $g$
- is a complex function of $g$
- is directly proportional to $g$
- is inversely proportional to $g$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$g=\frac{GM}{R^{2}}; M=\left(\frac{4}{3}\pi R^{3}\right)\rho$
$\therefore g=\frac{4G}{3} \frac{\pi R^{3}}{R^{2}}\,\rho$
$\Rightarrow g=\left(\frac{4G\pi R}{3}\right)\,\rho$
$\left(\rho=average\, density \right)$
$\Rightarrow g\,\propto\,\rho$ or $\rho\,\propto\,g$
Was this answer helpful?
1
0
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 AIEEE exam
- This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. It is not possible to make a sphere of capacity $1$ farad using a conducting material. It is possible for earth as its radius is $6.4 \times 10^6\,m$.
- AIEEE - 2012
- electrostatic potential and capacitance
- A steel wire can sustain $100\, kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
- AIEEE - 2012
- mechanical properties of solids
- The limiting line in Balmer series will have a frequency of (Rydberg constant, $R_{\infty}=3.29\times10^{15}$ cycles/s)
- AIEEE - 2012
- Electromagnetic Spectrum
- Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?
- The ratio of number of oxygen atoms (O) in 16.0 g ozone $(O_3), \,28.0\, g$ carbon monoxide $(CO)$ and $16.0$ oxygen $(O_2)$ is (Atomic mass: $C = 12,0 = 16$ and Avogadro?? constant $N_A = 6.0 x 10^{23}\, mol^{-1}$)
- AIEEE - 2012
- Mole concept and Molar Masses
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].