Question:
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius of the earth = 6400 km) :
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius of the earth = 6400 km) :
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At the poles the weight is mg; at the equator the effective gravity is reduced by the centrifugal term: \(g_{eq}=g-\omega^2R\) with \(\omega=2\pi/(24\ \mathrm{h})\).
Updated On: Oct 31, 2026
- 194.32 N
- 195.66 N
- 195.32 N
- 194.66 N
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The Correct Option is C
Solution and Explanation
Step 1: Mass of box \(m=\dfrac{196}{10}=19.6\) kg.
Step 2: \(\omega=\dfrac{2\pi}{86400}=7.27\times10^{-5}\) rad/s. \(\omega^2R=(7.27\times10^{-5})^2\times6.4\times10^{6}\approx0.0338\ \mathrm{m/s^2}\).
Step 3: \(g_{eq}=10-0.0338=9.9662\ \mathrm{m/s^2}\).
Step 4: Weight at equator \(=19.6\times9.9662\approx195.34\) N, closest to 195.32 N.
Answer: (C) 195.32 N
Step 2: \(\omega=\dfrac{2\pi}{86400}=7.27\times10^{-5}\) rad/s. \(\omega^2R=(7.27\times10^{-5})^2\times6.4\times10^{6}\approx0.0338\ \mathrm{m/s^2}\).
Step 3: \(g_{eq}=10-0.0338=9.9662\ \mathrm{m/s^2}\).
Step 4: Weight at equator \(=19.6\times9.9662\approx195.34\) N, closest to 195.32 N.
Answer: (C) 195.32 N
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