A thin wire of mass m and length l is bent to form a semicircle. The gravitational potential at the centre of the semicircle is

Question

A thin wire of mass m and length l is bent to form a semicircle. The gravitational potential at the centre of the semicircle is (A) -(π G m/l) (B) -(2 π G m/l) (C) (-3 π G m/l) (D) zero

Tardigrade Admin · Accepted Answer

At the centre, V=-(G m/r) but π r=l ⇒ V=-(π G m/l) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ef4a4403494ac42d3ef443e7e8b8c8a2-.png" />

Q. A thin wire of mass $m$ and length $l$ is bent to form a semicircle. The gravitational potential at the centre of the semicircle is

$- \frac{π G m}{l}$

$- \frac{2 π G m}{l}$

$\frac{- 3 π G m}{l}$

zero

At the centre,
$V = - \frac{G m}{r}$ but $π r = l$
$\Rightarrow V = - \frac{π G m}{l}$

Q. A thin wire of mass m and length l is bent to form a semicircle. The gravitational potential at the centre of the semicircle is

−lπGm​

−l2πGm​

l−3πGm​