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If ‘g’ is acceleration due to gravity on the earth and R is radius of the earth and angular speed of rotation of the earth about its axis is made to be $\sqrt{\frac{2g}{5R}}$ , then weight of a body at the equator decreases by

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50 %

40 %

60 %

75 %

answer is C.

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Detailed Solution

g^{|} = g - {Rw}^{2}

w = \sqrt{\frac{2g}{5R}}

$= g - R \times \frac{2g}{5R}$

$g^{|} = g - \frac{2g}{5} = \frac{3g}{5}$

Weight body decreases by $= g^{|} - g = g - \frac{3g}{5} = \frac{2g}{5} = 0.4 g$

$= 40%$

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