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19/09/2020 4:05 pm
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The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is : (h << R, where R is the radius of the earth)
(1) R2ω2 /4g
(2) R2ω2 /2g
(3) R2ω2 /8g
(4) R2ω2 /g
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19/09/2020 4:13 pm
(2) R2ω2 /2g
Explanation:
Both weight equally, it means effective 'g' is same for both
For A gA = g. -Rω2
For B gB = g. (1 - 2h/R)
gA = gB
Rω2 = 2g/R
∴ h = R2ω2 /2g