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Question:

The reading of a spring balance corresponds to 100N while situated at the north pole and a body is kept on it. The weight record on the same scale if it is shifted to the equator, is (take, g=10m/s^2) and radius of the earth, (R=6.4×10^3m).

99.66N

9766N

110N

106N

Solution:

Correct option is A. 99.66N
Let g' be the acceleration due to gravity at the equator and g that of the pole = g = 10m/s
Given that reading of spring balance at north pole, Mg = 100N ⇒ M = 10kg
g' = g - ω²R = 10 - (7.3 × 10⁻⁵)² × 6400 = 10 - 0.034 = 9.966m/s
Reading of spring balance at equator = Mg' = 10 × 9.966 = 99.66N