A thin rod of length L is bent to form a semi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The gravitational potential $V$ at a distance $r$ from a point mass $m$ is given by $V = -\frac{Gm}{r}$.For a continuous distribution of mass,the

Vedclass · Accepted Answer

$-\frac{\pi GM}{L}$

Vedclass · Answer

(D) The gravitational potential $V$ at a distance $r$ from a point mass $m$ is given by $V = -\frac{Gm}{r}$.For a continuous distribution of mass,the potential at the center of a circular arc is the same for every point on the arc because every point is at the same distance $r$ from the center.Given that the length of the rod is $L$ and it is bent into a semicircle,the radius $r$ of the semicircle is related to the length by the formula for the circumference of a semicircle: $\pi r = L$.Therefore,the radius is $r = \frac{L}{\pi}$.Since the total mass $M$ is distributed uniformly along the arc,the gravitational potential at the center is $V = -\frac{GM}{r}$.Substituting the value of $r$,we get $V = -\frac{GM}{(L/\pi)}$.Thus,the gravitational potential at the center is $V = -\frac{\pi GM}{L}$.

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the center of the circle?

Similar Questions

$A$ body of mass $m$ is raised through a height $h$ above the Earth's surface such that the increase in potential energy is $\frac{mgR}{5}$. The height to which the body is raised is ($R=$ radius of Earth,$g=$ acceleration due to gravity).

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

What is gravitational potential energy? What is zero potential energy?

Four particles each of mass $m$ are placed at four vertices of a rectangle having side lengths $3 l_o$ and $4 l_o$. The magnitude of the gravitational potential energy of the system in units of $\frac{Gm^2}{l_o}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module