Question

A. the masses m in the two figure have identical value for store which of the two system has a smaller gravitational potential? Why?
B. two particle of equal mass m go around a circle of radius r under the action of force due to their mutual gravitational attraction. Calculate the speed of each particle.

Answer 1

Answer:

Hey mate here is your answer.//

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Explanation:

A:Hey mate please keep the figure in your next question i will answer.

B:Given,

Masses of the two particles are m1=m2=m,

And radius of the two particles are r1=r2=R,

So ,The Gravitational force of attraction between the particles

F=G×m×m/R²..............=1,

Ans, centripital force F=m×v²/R.........=2,

From given condition (1) and (2)

Gmm/(2R)²=mv²/R,

v=Gm/4R=1/2√Gm/R,

So the speed of the each particle is

v=1/2√Gm/R.

Hope it helps you.//✔✔✔

Please do mark me as Brainliest.//

Answer 2

The second system has smaller gravitational potential energy.

Explanation:

The figure is attached.

We know that

Gravitational potential energy between two masses M and m, separated by a distance r is given by

$U=-\frac{GMm}{r}$

As shown, in figure (a), the distance between two masses M is

$\sqrt{r^2+r^2}=\sqrt{2r^2}=r\sqrt{2}$

Therefore the gravitational  potential energy is

$U=-\frac{GM^2}{r\sqrt{2}}$

In figure (b), the distance between the masses is

$2r$

Therefore the gravitational  potential energy is

$U'=-\frac{GM^2}{2r}$

Since $2r>r\sqrt{2}$

And the gravitational  potential energy has a negative sign

Therefore, in second case, the gravitational  potential energy will be smaller.

Hope this answer is helpful.

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