Question

Let $V_G$ and $E_G$ denote the gravitational potential and field respectively in a region, then choose the wrong statement.

• A. $V_G=0,E_G=0$
• B. $V_G\ne 0,E_G=0$
• C. $V_G=0,E_G\ne 0$
• D. $V_G\ne 0,E_G\ne 0$

Answer 1

The correct option is C $V_G=0,E_G\ne 0$

Gravitational field can be zero when the masses are placed such that the field due to each other cancel out or if all the masses are zero.
The relationship between gravitational field and potential is given by $$E=-\frac{dV}{dr}$$If the change in potential is zero i.e. potential is constant, the field will be zero.

Gravitational potential is zero, only when the masses are zero. Hence, it is not possible to have a non zero field with zero potential.

Hence option (c) is the correct option.

Key Concept - The relationship between gravitational field and potential is given by $$E=-\frac{dV}{dr}$$