If potential at the surface of earth is assigned zero value, then potential at centre of earth will be ( Mass =M, Radius =R)

Question

If potential at the surface of earth is assigned zero value, then potential at centre of earth will be ( Mass =M, Radius =R) (A) 0 (B) -(G M/2 R) (C) -(3 G M/2 R) (D) (3 G M/2 R)

Tardigrade Admin · Accepted Answer

The concept involved here is that,
Gravitational potential difference between any two points in a gravitational field is independent of the choice of reference. When potential at the infinity is assigned zero value,
Potential at the surface

= - \frac{GM}{R} = V_{s}

Potential at the centre

= - \frac{3 GM}{2 R} = V_{c}

V_{s} - V_{c} = - \frac{GM}{R} + \frac{3 GM}{2 R} = \frac{GM}{2 R}

Now, when potential at the surface is assigned zero value,

V_{s} - V_{c} = V_{s}^{'} - V_{c}^{'}

\Rightarrow \frac{GM}{2 R} = 0 - V_{c}^{'}

\Rightarrow V_{c}^{'} = - \frac{GM}{2 R}

Here,

V_{s}^{'}

and

V_{c}^{'}

are the new values of potential at the sum and centre respectively.

Q. If potential at the surface of earth is assigned zero value, then potential at centre of earth will be $($ Mass $= M$ , Radius $= R)$

0

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

$- \frac{3 GM}{2 R}$

$\frac{3 GM}{2 R}$

Q. If potential at the surface of earth is assigned zero value, then potential at centre of earth will be ( Mass =M, Radius =R)

0

−2RGM​

−2R3GM​

2R3GM​

Q. If potential at the surface of earth is assigned zero value, then potential at centre of earth will be $($ Mass $= M$ , Radius $= R)$

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

$- \frac{3 GM}{2 R}$

$\frac{3 GM}{2 R}$