Question

A planet moves in a elliptical path with sun is at one of its foci. Select the correct statement(s).

• A. In $QRP$ path work done by gravity is positive.
• B. Linear velocity of rotation from $Q$ to $P$ via $R$ decreases.
• C. In $PSQ$ path work done by gravity is negative.
• D. Gravitational potential energy increases in going from $P$ to $Q$ via $R$.

Answer 1

Answer: (A), (C), (D)

Gravitational potential energy increases in going from $P$ to $Q$ via $R$.

In path $QRP$, on going from $Q$ to $P$ via $R$, planet is going towards the sun (toward gravitational pull). Hence net work done by gravity is positive.

Similarly, in path $PSQ$ on going from $P$ to $Q$ via $S$, planet is going away from the sun (away from gravitational pull). Hence, net work done by gravity is negative. Therefore, options A and C are correct.
We know that angular momentum remain conserved for the planet.
So, $\Rightarrow mvr=$ constant
As $\therefore r\uparrow ,v\downarrow$

From $Q$ to $P$ via $R$, $r\downarrow \Rightarrow v\uparrow$
Therefore,option B is incorrect.

Further, gravitational potential energy,$U=-\frac{GMm}{r}$
So, as $r\uparrow ,U\uparrow$

From $P$ to $Q$ via $R$, $r\uparrow \Rightarrow U\uparrow$
Therefore, option (D) is correct.

OR

From conservation of angular momentum, When planet is at P velocity is maximum and when particle is at Q velocity is minimum.

While travelling along QRP velocity increases, hence Work done is positive.
While travelling along PSQ velocity decreases, hence Work done is negative.
Therefore, Option A,C are correct
Further, gravitational potential energy,$U=-\frac{GMm}{r}$
So, as $r\uparrow ,U\uparrow$

From $P$ to $Q$ via $R$, $r\uparrow \Rightarrow U\uparrow$
Therefore, option (D) is correct.