Question

Assertion :For the planets orbiting around the sun, angular speed, linear speed and K.E. changes with time, but angular momentum remains constant. Reason: No torque is acting on the rotating planet. So its angular momentum is constant.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Net torque acting on the rotating planet is zero i.e. $\tau =0$.

Using $\frac{dL}{dt}=\tau$

Thus $\tau =0$ $⟹$ $L=constant$

Hence angular momentum is constant.

So, reason statement is correct.

Now $L=mvr=constant$

$⟹$ $vr=constant$

Thus as the distance between sun and planet changes, linear speed of the planet changes and thus its kinetic energy also changes.

Also using $L=m{r}^{2}w=constant$

$⟹$ $r^{2}w=constant$

Thus as the distance between sun and planet changes, angular speed of the planet changes.

Hence assertion statement is also correct and reason explains the assertion very well.