Question

Assertion :The earth is slowing down and as a result the moon is coming nearer to it. Reason: The angular momentum of the earth moon system is not conserved.

• 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 C Assertion is correct but Reason is incorrect

The angular momentum of earth-moon system will be conserved because no torque is acting on it.
So, $\tau =\frac{dL}{dt}$
If $\tau =0,\frac{dL}{dt}=0\Rightarrow L$ is constant.
Thus angular momentum is constant. So reason is wrong.
So, we get $I_1{\omega }_1=I_2{\omega }_2$
where $I_1$ & $I_2$ are momentia of inertia of earth and moon & ${\omega }_1$ & ${\omega }_2$ are their angular velocities. If earth slows down ${\omega }_1$ will be decreased. So, $I_2$ will be decreased if we take ${\omega }_2$ to remain constant.
Now, $I_2=m_2{r}_2^2$

where $m_2$ is mass of moon & $r_2$ is radius of moon's orbit. So $r_2$ will be reduced to reduce $I_2$. Hence moon will come near to the earth. Hence assertion is right.