A body of mass m is kept at a small height h | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The gravitational potential energy $U$ of a body of mass $m$ at a distance $r$ from the center of the Earth (mass $M$) is given by $U = -\frac{GMm

Vedclass · Accepted Answer

$-\frac{GMm}{R} + mgh$

Vedclass · Answer

(B) The gravitational potential energy $U$ of a body of mass $m$ at a distance $r$ from the center of the Earth (mass $M$) is given by $U = -\frac{GMm}{r}$.Here,the body is at a height $h$ above the surface of the Earth,so its distance from the center is $r = R + h$.Therefore,the potential energy is $U = -\frac{GMm}{R+h}$.Note: If $h$ is very small compared to $R$,we can approximate this using the Taylor expansion: $U = -\frac{GMm}{R(1 + h/R)} \approx -\frac{GMm}{R}(1 - h/R) = -\frac{GMm}{R} + \frac{GMmh}{R^2}$.Since $g = \frac{GM}{R^2}$,this becomes $U \approx -\frac{GMm}{R} + mgh$.

Column-$I$	Column-$II$
$(1)$ Can never be positive.	$(a)$ Escape velocity
$(2)$ Reason for negative potential energy of galaxies.	$(b)$ Gravitational potential energy
	$(c)$ The nature of force between different galaxies is attractive.

$A$ body of mass $m$ is kept at a small height $h$ above the ground. If the radius of the earth is $R$ and its mass is $M$,the potential energy of the body and earth system (with $h = \infty$ being the reference position) is

Similar Questions

Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

Two bodies of masses $m$ and $9m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them,where the gravitational field is zero,is ($G$ is the universal gravitational constant).

Two point masses having mass $M$ and $4 M$ are placed at a distance $r$. The gravitational potential at a point,where the gravitational field intensity is zero,is ..............

Match Column-$I$ with Column-$II$.
Column-$I$ Column-$II$
$(1)$ Can never be positive. $(a)$ Escape velocity
$(2)$ Reason for negative potential energy of galaxies. $(b)$ Gravitational potential energy
$(c)$ The nature of force between different galaxies is attractive.

Define gravitational potential energy. Obtain the formula for the gravitational potential energy of a body of mass $m$ at a distance $r$ $(r > R_E)$ from the centre of the Earth.

Vedclass Test Series

Exam Paper Generator

Online Exam Module