First slide

Acceleration due to gravity and its variation

Question

A box weighs 196N 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 $m s^{- 2}$ at the north pole and the radius of the earth = 6400km)

Difficult

A

194.32 N
B

194.66 N
C

195.32 N
D

195.66 N

Solution

At pole, weight $= m g = 196$
$\Rightarrow m = 19.6 k g$
At equator, weight $= m g - m ω^{2} R$ $= 196 - (19.6) {[\frac{2 π}{86400}]}^{2} \times 6400 \times 10^{3} = 196 - \frac{19.6 (39.44) 6400000}{7464960000} = 196 - 0.663 = 195.32 N$

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