Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: If the ice on the polar caps of the earth melts, then length of day will increase. Reason: Moment of inertia of earth increases, as ice on polar caps melts.A) If both assertion and reason are true and reason is the correct explanation of assertion
B) If both assertion and 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
Correct Answer: A
Solution :
When the ice on the polar caps melts, the mass concentrated near the axis of rotation is spread out. The moment of inertia of system increases. Since, no external torque acts on the system. \[I\omega =\text{constant}\] Therefore, if \[I\] increases, the angular speed will decrease. So, the time period of rotation of earth\[\left( T=\frac{2\pi }{\omega } \right)\] increases i.e., the duration of the day will increase. Hence, option (a) is correct.
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