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For the Newton's laws to hold true at the Earth's equator, if c is the value of correction to the gravitational acceleration (g) that should be subtracted from g, then which one of the following is correct?
Explanation
Newton's laws of motion are strictly applicable in inertial (non-accelerating) frames of reference. Since the Earth rotates about its axis, it is a non-inertial frame. To apply Newton's laws at the Earth's equator as if it were an inertial frame, we must account for the centrifugal acceleration (c) acting radially outward.
The effective acceleration due to gravity (g') is given by:
g' = g - ω2R
Where c = ω2R is the correction term.
- Angular velocity of Earth (ω) = 2π / 86400 ≈ 7.27 × 10-5 rad/s
- Equatorial radius of Earth (R) ≈ 6.378 × 106 m
Calculating c:
c = (7.27 × 10-5)2 × 6.378 × 106 ≈ 0.0337 m/s2
Since 0.0337 > 0.03, the value of c falls into the range specified in option D.
SIMILAR QUESTIONS
Which one among the following statements is not correct ?
The acceleration due to gravity ‘g’ for objects on or near the surface of earth is related to the universal gravitational constant 4G’ as (‘M’ is the mass of the earth and ‘R’ is its radius):
Statement I: The acceleration due to gravity decreases with increase in height from the surface of the Earth. Statement I : The acceleration due to gravity is inversely proportional to the square of the distance from the centre of the Earth.
Which one among the following is the correct value of the gravitational force of the Earth acting on a body of mass 1 kg?
Assertion (A): The Equatorial regions bulge outwards by about 21 kilometre compared to Poles.
Reason (R): Earth’s slow rotation reduces the effect of gravity around the Equator.