The gravitational potential due to the earth at infinite distance from it is zero. Let the gravitational potential at a point P be -5J / kg . Suppose, we arbitrarily assume the gravitational potential at infinity to be + 10 J / kg , then the gravitational potential at P will be

The correct option is +5 J / kg.

To understand why this is the case, we look at the relationship between gravitational potential at a point and the reference point (which is typically infinity).

Gravitational potential at a point is defined relative to a reference point. The absolute value of potential changes based on our choice of the reference level, but the potential difference between any two points is a physical quantity and must remain constant.

Let us denote the initial potential at infinity as:

$V_{\infty }=0\text{J/kg}$

And the initial potential at point P as:

$V_P=-5\text{J/kg}$

The difference in gravitational potential between point P and infinity is:

$\Delta V=V_P-V_{\infty }$

$\Delta V=-5-0=-5\text{J/kg}$

If we arbitrarily change the reference potential at infinity to a new value:

$V_{\infty }^{\prime }=+10\text{J/kg}$

Since the potential difference between the two points must remain unchanged, we set up the equation:

$V_P^{\prime }-V_{\infty }^{\prime }=\Delta V$

Substituting the new value for the reference potential at infinity and the constant potential difference:

$V_P^{\prime }-10=-5$

Solving for the new potential at point P:

$V_P^{\prime }=-5+10=+5\text{J/kg}$

Therefore, the new gravitational potential at point P will be +5 J/kg.