Taking the gravitational potential at a point | vedclass

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Question

(B) The gravitational potential $V$ at a point is defined as the work done per unit mass in bringing a test mass from a reference point to that point.

Vedclass · Accepted Answer

$+5$

Vedclass · Answer

(B) The gravitational potential $V$ at a point is defined as the work done per unit mass in bringing a test mass from a reference point to that point.The potential difference between a point $A$ at distance $r$ and a reference point at infinity is given by $V_A - V_{\infty} = -\int_{\infty}^{r} \vec{E} \cdot d\vec{r} = -\frac{GM}{r}$.Case $(i)$: When the potential at infinity is $V_{\infty} = 0$,the potential at point $A$ is $V_A = -5 \, unit$.Thus,$-5 - 0 = -\frac{GM}{r}$,which implies $-\frac{GM}{r} = -5$.Case $(ii)$: When the potential at infinity is $V_{\infty}' = +10 \, unit$,the potential at point $A$ becomes $V_A'$.The potential difference remains the same because it depends only on the mass and the distance: $V_A' - V_{\infty}' = -\frac{GM}{r}$.Substituting the values: $V_A' - 10 = -5$.Therefore,$V_A' = -5 + 10 = +5 \, unit$.

Taking the gravitational potential at a point at an infinite distance away as zero,the gravitational potential at a point $A$ is $-5 \, unit$. If the gravitational potential at a point at an infinite distance away is taken as $+10 \, units$,the potential at point $A$ is ......... $unit$.

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