Question:
The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown in the figure.
The correct figure is
The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown in the figure.
The correct figure is
Updated On: Jul 13, 2024
- $(i)$
- $(ii)$
- $(iii)$
- $(iv)$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The acceleration due to gravity at a depth $d$ below the surface of earth is
$g' = g\left(1-\frac{d}{R}\right) = g\left(\frac{R-d}{R}\right) = g \frac{r}{R} \quad\ldots\left(i\right)$
where $R - d = r =$ distance of location from the centre of the earth. When $r = 0$, $g' = 0$
From $\left(i\right)$, $g \propto r$ till $R = r$, for which $g' =g$
For $r > R$, $g' = \frac{gR^{2}}{\left(R+h\right)^{2}} = \frac{gR^{2}}{r^{2}}$
or $g' \propto \frac{1}{r^{2}}$
Here, $R + h = r$
Therefore, the variation of $g$ with distance $r$ from centre of earth will be as shown in figure.
$g' = g\left(1-\frac{d}{R}\right) = g\left(\frac{R-d}{R}\right) = g \frac{r}{R} \quad\ldots\left(i\right)$
where $R - d = r =$ distance of location from the centre of the earth. When $r = 0$, $g' = 0$
From $\left(i\right)$, $g \propto r$ till $R = r$, for which $g' =g$
For $r > R$, $g' = \frac{gR^{2}}{\left(R+h\right)^{2}} = \frac{gR^{2}}{r^{2}}$
or $g' \propto \frac{1}{r^{2}}$
Here, $R + h = r$
Therefore, the variation of $g$ with distance $r$ from centre of earth will be as shown in figure.
Was this answer helpful?
0
0
Top Questions on 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
- 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
- An astronaut experiences weightlessness in space satellite because
- KEAM - 2025
- Physics
- Gravitation
- Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
(A) A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
(R) The mass of the pendulum remains unchanged at Earth and the other planet.
In light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- Gravitation
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant. In the light of the above statements, choose the most appropriate answer from the options given below :- JEE Main - 2025
- Physics
- Gravitation
View More Questions
Questions Asked in NEET exam
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :
- NEET (UG) - 2025
- Moment Of Inertia
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
- A microscope has an objective of focal length \(f_o = 2\) cm and an eyepiece of focal length \(f_e = 4\) cm. The tube length of the microscope is \(L = 40\) cm. If the distance of distinct vision of eye is \(D = 25\) cm, the magnification in the microscope is:
- NEET (UG) - 2025
- Optical Instruments
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- Given below are two statements:
Statement I: Fig fruit is a non-vegetarian fruit as it has enclosed fig wasps in it.
Statement II: Fig wasp and fig tree exhibit a mutual relationship as the fig wasp completes its life cycle in the fig fruit and the fig fruit gets pollinated by the fig wasp.
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].