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

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, τ=dLdt
If τ=0,dLdt=0L is constant.
Thus angular momentum is constant. So reason is wrong.
So, we get I1ω1=I2ω2
where I1 & I2 are momentia of inertia of earth and moon & ω1 & ω2 are their angular velocities. If earth slows down ω1 will be decreased. So, I2 will be decreased if we take ω2 to remain constant.
Now, I2=m2r22
where m2 is mass of moon & r2 is radius of moon's orbit. So r2 will be reduced to reduce I2. Hence moon will come near to the earth. Hence assertion is right.

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