Assertion : For the planets orbiting around the sun, angular spee… - Vidyadip

MCQ

$Assertion$ : 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.

✓
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

✓

Answer

Correct option: A.

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

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

Using $\frac{d L}{d t}=\tau$

Thus $\tau=0 \Longrightarrow L=$ constant

Hence angular momentum is constant.

So, reason statement is correct.

Now $L=m v r=$ constant

$\Longrightarrow v r=$ 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

$\Longrightarrow r^{2} w=$ 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.

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