If the polar ice caps melt and spread uniformly . . .

Question : If the polar ice caps melt and spread uniformly, how will the length of the day be affected?

OR

If polar ice caps melt, then the angular velocity of rotation of earth

(a) increases

(b) decreases

(d) becomes zero

Assertion (A) : If polar ice melts, days will be longer.

Reason (R) : Moment of inertia decreases and thus angular velocity increases.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false but Reason (R) is true.

Solution :

Short Answer :

If the polar ice caps melt and spread uniformly, the length of the day will increase. This is because the Earth's moment of inertia will increase and as per the law of conservation of angular momentum when moment of inertia increases then the annular velocity if the earth will decreases so the earth will rotate slowly and hence the length of the day will increases.

Detailed Explanation :

When the polar ice caps melt, the water will spread out towards the equator, which is farther from the Earth's axis of rotation. This will increase the Earth's moment of inertia.

Moment of Inertia (I) is directly proportional to square of the distance (r²)

According to the law of conservation of angular momentum, the Earth's angular momentum (L) must remain constant.

L = constant

Iω=constant

So, if the Earth's moment of inertia increases, its rotational speed (angular velocity) must decrease in order to keep angular momentum constant. This means that the length of the day will increase.

The exact amount by which the length of the day would increase if the polar ice caps melted depends on a number of factors, including the amount of ice that melts and how it is distributed around the globe. However, scientists estimate that it would be a very small increase, on the order of a few milliseconds per day.