If the potential at the surface of the Earth | vedclass

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

Question

(B) The gravitational potential difference between any two points in a gravitational field is independent of the choice of reference point.When the po

Vedclass · Accepted Answer

$-\frac{GM}{2R}$

Vedclass · Answer

(B) The gravitational potential difference between any two points in a gravitational field is independent of the choice of reference point.When the potential at infinity is assigned a zero value:Potential at the surface,$V_s = -\frac{GM}{R}$Potential at the center,$V_c = -\frac{3GM}{2R}$The potential difference between the surface and the center is:$V_s - V_c = -\frac{GM}{R} - (-\frac{3GM}{2R}) = -\frac{GM}{R} + \frac{3GM}{2R} = \frac{GM}{2R}$Now,if the potential at the surface is assigned a zero value $(V_s' = 0)$,let the new potential at the center be $V_c'$.Since the potential difference remains constant:$V_s - V_c = V_s' - V_c'$$\frac{GM}{2R} = 0 - V_c'$$V_c' = -\frac{GM}{2R}$Therefore,the potential at the center is $-\frac{GM}{2R}$.

If the potential at the surface of the Earth is assigned a zero value,then the potential at the center of the Earth will be (Mass $= M$,Radius $= R$).

Similar Questions

Consider two configurations of a system of three particles of masses $m, 2m$ and $3m$. The work done by an external agent in changing the configuration of the system from figure $(i)$ to figure $(ii)$ is:

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.

If the gravitational field intensity at a point is given by $E = K/x^3$,what is the gravitational potential at that point?

What is the magnitude of potential energy at infinity distance?

What is potential energy and gravitational potential energy? Write the dimensional formula of gravitational potential energy.

Vedclass Test Series

Exam Paper Generator

Online Exam Module