An imaginary galaxy is considered to consist of $N$ stars each of mass $M$ and with each pair of stars at a mutual separation of $R .$ If $N = 4, R = 10^{21} m, M = 2 \times 10^{30} k g$ , find out the gravitational potential energy of galaxy.

Open in App

Solution

The gravitational energy is given by
$U = - G \sum I, J = 1 N \frac{m_{1} m_{1}}{r_{I J}}$
Here, $m_{i} = m_{j} = M = 2 \times 10^{30} k g s$
Then, $U = - \frac{1}{2} G (N - 1) N \frac{M^{2}}{R}$
$= - \frac{(6.67 \times 10^{- 11} \times 4) \times (4 - 1) \times (2 \times 10^{30})^{2}}{2 \times 10^{21}}$
$= - 1.6 \times 10^{30} J (a p p r o x .)$

Suggest Corrections

Similar questions

Q. A double star is a system of two stars of masses m and

2

m, rotating about their centre of mass only under their mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to.

Q. A very long (length

L

) cylindrical galaxy is made of uniformly distributed mass and has radius

R (R << L)

. A star outside the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is

T

and its distance from the galaxy s axis is

r

, then:

Q. A very long (length

L

) cylindrical galaxy is made of uniformly distributed mass and has radius

R (R << L)

. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is

t

and its distance from the galaxy's axis is

r

, then

In a binary star system, two stars of masses m and 2m distance r apart are revolving about their common centre of mass under their mutual gravitational attraction.

The ratio of kinetic energy of two stars is

Q. A double star consists of two stars having masses M and

2

M. The distance between their centres is equal to r. They revolve under their mutual gravitational interaction. Then, which of the following statements are not correct?

Join BYJU'S Learning Program

An imaginary galaxy is considered to consist of N stars each of mass M and with each pair of stars at a mutual separation of R. If N=4,R=1021m,M=2×1030kg, find out the gravitational potential energy of galaxy.

The gravitational energy is given byU=−G∑I,J=1Nm1m1rIJHere, mi=mj=M=2×1030kgsThen, U=−12G(N−1)NM2R=−(6.67×10−11×4)×(4−1)×(2×1030)22×1021=−1.6×1030J(approx.)

An imaginary galaxy is considered to consist of $N$ stars each of mass $M$ and with each pair of stars at a mutual separation of $R .$ If $N = 4, R = 10^{21} m, M = 2 \times 10^{30} k g$ , find out the gravitational potential energy of galaxy.