Question

If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$ Taking the reference point to be at $r =2\, cm$ with gravitational potential $V =10 \,J / kg$ Find the gravitational potential at $r =3\, cm$ in SI unit (Given, that $K =6 \,Jcm / kg$)

• A. 11
• B. 10
• C. 12
• D. 9

Answer 1

The Correct Option is B

$-\frac{dV}{dr}=-\frac{k}{r^2}\Rightarrow \underset{10}{\overset{V}{\int }}dV=\underset{2}{\overset{3}{\int }}\frac{k}{r^2}dr$
$V-10=k\left[\frac{1}{2}-\frac{1}{3}\right]$
$V-10=\frac{k}{6}\Rightarrow V=11\text{volts}$