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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
$Assertion$ : 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
    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.
  • ✓
    If the Assertion is correct but Reason is incorrect.
  • D
    If both the Assertion and Reason are incorrect.
✓

Answer

Correct option: C.
If the Assertion is correct but Reason is incorrect.
c
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.

or angular momentum is constsnt. So Reason is incorrect.

so, ${I_1}{\omega _1} = {I_2}{\omega _2}$

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 $, will be decreased. So,${I_2}$ will be decreased if we take ${\omega _2}$ to remain constant.

${I_2} = {m_2}r_2^2$ where $m_2$ is mass of moon & $r_2$ is radius of moon' orbit, $r_2$ will be reduced to redice $I_2$ Hence moon will come near to the earth. Hence Assertion is correct.

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