If g is the acceleration due to gravity on th | vedclass

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

Question

(C) The gravitational potential energy of an object of mass $m$ at the surface of the earth is given by $U_{1} = -\frac{GMm}{R}$.At a height $h = R$ f

Vedclass · Accepted Answer

$\frac{1}{2} mgR$

Vedclass · Answer

(C) The gravitational potential energy of an object of mass $m$ at the surface of the earth is given by $U_{1} = -\frac{GMm}{R}$.At a height $h = R$ from the surface,the distance from the center of the earth is $r = R + h = R + R = 2R$.The potential energy at this height is $U_{2} = -\frac{GMm}{2R}$.The gain in potential energy is $\Delta U = U_{2} - U_{1} = -\frac{GMm}{2R} - (-\frac{GMm}{R}) = \frac{GMm}{R} - \frac{GMm}{2R} = \frac{GMm}{2R}$.Since the acceleration due to gravity at the surface is $g = \frac{GM}{R^{2}}$,we have $GM = gR^{2}$.Substituting this into the expression for $\Delta U$:$\Delta U = \frac{1}{2} \frac{(gR^{2})m}{R} = \frac{1}{2} mgR$.

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.

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Similar Questions

What is gravitational potential energy? What is zero potential energy?

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$ (as shown in the figure) in the gravitational field of the point mass '$m$',find the correct relation between '$W_1$','$W_2$' and '$W_3$'.

Give the difference between gravitational potential energy and gravitational potential.

$A$ thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$. The work required to take a unit mass from point $P$ on its axis to infinity 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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module