Question

Read the assertion and reason carefully to mark the correct option out of the options given below :

Assertion : Radius of circular orbit of a satellite is made two times, then it areal velocity will also become two times.

Reason : Areal velocity is given as $\frac{dA}{dt}=\frac{L}{2m}=\frac{mvr}{2m}$

• A. If both assertion and reason are true and the reason is the correct explanation of the assertion
• B. If both assertion and reason are true but reason is not the correct explanation of the assertion
• C. If assertion is true but reason is false
• D. If assertion is false but reason is true

Answer 1

Answer: (D)

If assertion is false but reason is true

Areal velocity $\frac{dA}{dt}=\frac{L}{2m}=\frac{mvr}{2m}$

As there is no external torque, thus $L=constant$

Now if radius of orbit increases by 2 times then the velocity of satellite will get reduced by 2 times so as to make $L$ to be constant.

Hence overall, increasing $r$ has no effect on areal velocity.

So the assertion is false.