A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R then change in gravitational potential energy is :
A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R then change in gravitational potential energy is :
\(\frac{mgR}{4}\)
\(\frac{2}{3}mgR\)
\(\frac{3}{4}mgR\)
\(\frac{mgR}{2}\)
The Correct Option is C
Solution and Explanation
The correct option is (C) : \(\frac{3}{4}mgR\)
Change in G.P.E. = final energy – initial energy
= \(-\frac{GMm}{4R}+\frac{GMm}{R}\) = \(\frac{GMm}{R}[\frac{1}{\frac{1}{4}}]\)
\(\frac{3}{4}\frac{GMm}{R}=\frac{3}{4}\frac{GM}{R^2}mR=\frac{3}{4}gmR\)
Top Questions on Gravitation
- Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2m, then they will collide after ______ seconds.
- JEE Main - 2025
- Physics
- Gravitation
- A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
- JEE Main - 2025
- Physics
- Gravitation
Match the LIST-I with LIST-II
\[ \begin{array}{|l|l|} \hline \text{LIST-I} & \text{LIST-II} \\ \hline \text{A. Gravitational constant} & \text{I. } [LT^{-2}] \\ \hline \text{B. Gravitational potential energy} & \text{II. } [L^2T^{-2}] \\ \hline \text{C. Gravitational potential} & \text{III. } [ML^2T^{-2}] \\ \hline \text{D. Acceleration due to gravity} & \text{IV. } [M^{-1}L^3T^{-2}] \\ \hline \end{array} \]
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
- Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): \begin{itemize} \item[(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. \item[(R)] The mass of the pendulum remains unchanged at Earth and the other planet. \end{itemize} In light of the above statements, choose the correct answer from the options given below:
- JEE Main - 2025
- Physics
- Gravitation
Questions Asked in NEET exam
- In some appropriate units, time (t) and position (x) relation of a moving particle is given by \(t = \alpha x^2 + \beta x\). The acceleration of the particle is :
- NEET (UG) - 2025
- Kinematic equations for uniformly accelerated motion
The output (Y) of the given logic implementation is similar to the output of an/a …………. gate.
- NEET (UG) - 2025
- Logic gates
- Two identical point masses P and Q, suspended from two separate massless springs of spring constants \(k_1\) and \(k_2\), respectively, oscillate vertically. If their maximum velocities are the same, the ratio of the amplitude of P to the amplitude of Q is :
- NEET (UG) - 2025
- Waves and Oscillations
- A particle of mass \(m\) is moving around the origin with a constant speed \(v\) along a circular path of radius \(R\). When the particle is at \( (0, R) \), its velocity is \( \mathbf{v} = -v \hat{\mathbf{i}} \). The angular momentum of the particle with respect to the origin is :
- NEET (UG) - 2025
- The Angular Momentum
- The radius of Martian orbit around the Sun is about 1.5 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?
- NEET (UG) - 2025
- Kepler’s laws
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].