Asteroids X, Y, and Z have equal mass of 7.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 7.0 kg each. They orbit around a planet with M=4.20E+24 kg. The orbits are in the plane of the paper and are drawn to scale.

In the statements below, TE is the total mechanical energy, KE is the kinetic energy, and PE is the potential energy.

The KE of Z at a is .... that at u
The PE of Y at s is .... the PE of Z at u
The TE of X is .... the TE of Y
The PE of Y at s is .... the PE of Z at s
The PE of X at u is .... that at i
The PE of Y at s is .... the PE of X at r
The speed of X at c is .... that at i
The TE of Z is .... the TE of Y

Options are >, <, =

Explanation / Answer

1)The KE of Z at a is EQUAL TO that at u.

since, the distance remains same from the planet.

2)The PE of Y at s is EQUAL TO the PE of Z at u.

again the distance of these two points from the planet is same.

3)The total energy(TE) of X is LESS THAN the TE of Y.

since Y is more distant than X from the planet.

4)The PE of Y at s is EQUAL TO the PE of Z at s.

since PE = G M m/r ; M is same for both Y and Z.

5)PE of X at u is GREATER THAN the PE of X at i

since, i is far than u.

6)PE of Y at s is GREATER THAN the PE of X at r

distance of r is more than s

7)The Speed of X at c is GREATER THAN that at i

since, = sqrt (G M/R)

R is more for i.

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