Question

A body of mass 100 kg is weighed at the North Pole and at the equator with a spring scale. What is the scale reading at these two points? Assume that g=9.83m/s2 at the pole.

a) 980 N at both points
b) 980 N at the North Pole and less than 980 N at the equator
c) Less than 980 N at both points
d) 980 N at the North Pole and more than 980 N at the equator

Answer 1

The weight of a 100 kg body would be 980 N at the North Pole, where gravity is 9.83 m/s². At the equator, the weight would be less than 980 N due to Earth's rotation and its larger radius at the equator.

Step-by-step explanation:

The question concerns the weight measurement of an object at different locations on Earth, specifically comparing the scale readings at the North Pole and the equator. The acceleration due to gravity is slightly different at these two points due to Earth's rotation and the flattening of the planet at the poles.

The weight of a body on Earth is calculated using the formula w = mg, where w is the weight, m is the mass of the body, and g is the local acceleration due to gravity. At the North Pole, where g is given as 9.83 m/s2, the weight of the 100 kg body would be w = (100 kg)(9.83 m/s2) = 983 N, slightly higher than the standard Earth gravitational acceleration due to flattening at the poles.

However, at the equator, the acceleration due to gravity is slightly less than at the poles because of the centrifugal force due to Earth's rotation, which effectively lessens the gravitational pull. Also, the equatorial radius of Earth is larger than at the poles, causing gravity to be weaker. Therefore, the scale would read slightly less than 980 N at the equator. The correct answer is therefore b) 980 N at the North Pole and less than 980 N at the equator.