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The earth is slowing down and as a resul...

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

A

If both assertion and reason are true and reason is the true explanation of assertion.

B

If both assertion and reason are reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false

D

If both assertion and reason are false.

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Earth is not slowing down. Angular momentum of earth-moon system is conserved, had it not been so, then Kepler's second law of planetary motion would not have been valid.
Kepler's second law states that
`(dA)/(dt) = (J)/(2m)` = constant
where `(dA)/(dt)` is a real speed, `J` is angular momentum, `m` is mass.
Hence, angular momentum is constant.
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Knowledge Check

  • Centre of mass of the earth-moon system lies

    A
    on the surface of the earth
    B
    on the surface of the moon
    C
    with in the earth
    D
    at the midpoint of the line joinining their centres

  • Assertion :- The mechanical energy of earth-moon system remains same when a another heavenly body passes nearby the earth - moon system. Reason :- Force exerted by heavenly body on the earth - moon system is non - conservative.

    A
    If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
    B
    If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
    C
    If Assertion is True but the Reason is False.
    D
    If both Assertion & Reason are False

  • The conservation of angular momentum, which corresponds to the conservation of linear momentum states that the angular momentum about an axis of a given rotating body of system of bodies is constant, if no external torque acts about that axis. The earth rotates about an axis passing through its geographic north and south poles with a period of one day. If its is struck by meteorites, then since action and reaction are equal, no external couple acts on the earth and metorites. Their total angular momentum is thus conserved. Neglecting the angular momentum of the meteorites about the earths axis before collision compared with that of the earth, then angular momentum of (earth + metorites) after collision = angular momentum of earth before collision. Since the effective mass of the earth has increassed after collision, the moment of inertia has increased. So the earth will slow down slightly. In the pervious problem, velocity of the bullet just after the collision is

    A
    u
    B
    `(8 m u)/((8m + M))`
    C
    `(8 m u)/(8m + 3M)`
    D
    `(8 m u)/(8m + 3M)`

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