Question

20. Find the potential energy of a system of four particles, each of mass m, placed at the ve
square of side L. Obtain the potential at the centre of the sphere.​

Answer 1

Answer:

For a mass of

m

potential energy of a test mass at distance r is given as

(G⋅mr)

Total potential energy of the system is G

m2l×4+2

⋅Gm2√2l

or, 4Gm2l+√2Gm2l( Due to 4 mass at the vertices and 2 diagonally present,length of diagonal is

√

2

l

)

Distance of each mass from the centre is =length of diagonal/2 i.e

l

√

2

So,potential energy at the centre for 4 such mass is

⎛

⎜

⎝

G

m

l

√

2

⋅

4

⎞

⎟

⎠

i.e

4

√

2

G

m

l