What should be the velocity of earth due to r | vedclass

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Question

(c) Weight of the body at equator = $\frac{3}{5}$ of initial weight  

$g' = \frac{3}{5}g$ (because mass remains constant) 

$g'

Vedclass · Accepted Answer

$7.8 	imes {10^{ - 4}}\,rad/\sec $

Vedclass · Answer

(c) Weight of the body at equator = $\frac{3}{5}$ of initial weight  

$g' = \frac{3}{5}g$ (because mass remains constant) 

$g' = g - {\omega ^2}R{\cos ^2}\lambda $  $&rArr;$  $\frac{3}{5}g = g - {\omega ^2}R{\cos ^2}(0^\circ )$ 

$&rArr;$ ${\omega ^2} = \frac{{2g}}{{5R}}$  $&rArr;$  $\omega = \sqrt {\frac{{2g}}{{5R}}} = \sqrt {\frac{{2 	imes 10}}{{5 	imes 6400 	imes {{10}^3}}}} $ = $7.8 	imes {10^{ - 4}}\frac{{rad}}{{\sec }}$

What should be the velocity of earth due to rotation about its own axis so that the weight at equator become $3/5$ of initial value. Radius of earth on equator is $ 6400\, km$

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