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)

Engineering

Physics

Gravitational Acceleration

Question

$\frac{R^{2} ω^{2}}{2 g}$

$\frac{R^{2} ω^{2}}{4 g}$

$\frac{R^{2} ω^{2}}{8 g}$

$\frac{R^{2} ω^{2}}{g}$

Both weight equally, it means effective 'g' is same for both

For A g_A = g . – Rω²

For B $g_{B} = g \cdot (1 - \frac{2 h}{R})$

g_A = g_B

${Rω}^{2} = \frac{2 g}{R}$

$∴ h = \frac{R^{2} ω^{2}}{2 g}$

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