Home
Class 11
PHYSICS
Four particles each of mass m are placed...

Four particles each of mass m are placed at the vertices of a square of side l. the potential at the centre of square is

A

`(-sqrt2Gm^(2))/(l)(2-(1)/(sqrt(2)))`

B

`(-2Gm^(2))/(l)(2+(1)/(sqrt(2)))`

C

`(-sqrt2Gm^(2))/(l)(sqrt2-(1)/(sqrt(2)))`

D

`(-2Gm^(2))/(l)(sqrt2+(1)/(sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Refer to Fig. `Ac = BD = lsqrt(2)`

Total energy of the system of four masses placed at the vertices of square will be
`=W_(12) + (W_(13) + W_(23)) + (W_(14) + W_(24)) + W_(34)`
`= - [(Gm^(2))/(l) + (Gm^(2))/(lsqrt(2)) + (Gm^(2))/(l) + (Gm^(2))/(l) + (Gm^(2))/(lsqrt(2)) + (Gm^(2))/(l)]`
`= - (2Gm^(2))/(l) [2 + (1)/(sqrt(2))]`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the potential energy of a system of four particles each of mass 2m kept at the vertices of a square of side x. Also find the potential at the centr of the square.

Four point charges are placed at the corners of a square of side l. Calculate potential at the centre of square.

Four charges 10^(-5) , -2times10^(-5) , +3times10^(-5) and 2times10^(-5) coulomb are placed at the four corners of a square of side 1m the potential at the centre of the square is...

Find the gravitational potential energy of a system of four particles, each of mass m placed at the verticles of a square of side l . Also obtain the gravitaitonal potential at centre of the square.

Four particles each of mass m are placed at the corners of a square of side length l . The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is

Four particles, each of mass 1kg are placed at the corners of a square of side 1m in the XY plane. If the point of intersecting of the diagonals of the square is taken as the origin, the co-ordinates fo the centre of mass are

Four particles each of mass m are placed at the corners of a square of side length l . The radius of gyration of the system the moment of inertia of four bodies about an axis passing through any side of frame is

Four particles each of mass m are placed at the corners of a square of side length l . The radius of gyration of the system the moment of inertia of four bodies about an axis passing through opposite corners of frame is

Four particles each of mass m are placed at the corners of a square of side length l . The radius of gyration of the system the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner is

Four particles each of mass m are kept at the four vertices of a square of side 'a' . Find graitational potential energy of this system.