The gravitational potential energy of a body of mass ‘m’ at the earth’s surface $-mg{R}_{\mathcal{e}}$. Its gravitational potential energy at a height ${R}_{\mathcal{e}}$ from the earth’s surface will be (Here ${R}_{\mathcal{e}}$  is the radius of the earth)

(a)       $-2mg{R}_{\mathcal{e}}$              (b)        $2mg{R}_{\mathcal{e}}$

(c)       $\frac{1}{2}mg{R}_{\mathcal{e}}$               (d)        $-\frac{1}{2}mg{R}_{\mathcal{e}}$

Concept Videos :-

#21 | Gravitational Potential Energy
#22 | Problem on Gravitational Potential Energy
#23 | Problem on Gravitational Potential Energy
#24 | Self Potential Energy of Shell & Solid Sphere
#30 | Question on Potential Energy

Concept Questions :-

Gravitational potential energy

(d) $∆U={U}_{2}-{U}_{1}=\frac{mgh}{1+\frac{h}{{R}_{\mathcal{e}}}}=\frac{mg{R}_{\mathcal{e}}}{1+\frac{{R}_{\mathcal{e}}}{{R}_{\mathcal{e}}}}=\frac{mg{R}_{\mathcal{e}}}{2}$

$⇒{U}_{2}+\left(mg{R}_{\mathcal{e}}\right)=\frac{mg{R}_{\mathcal{e}}}{2}⇒{U}_{2}=-\frac{1}{2}mg{R}_{\mathcal{e}}$

Difficulty Level:

• 19%
• 14%
• 18%
• 51%