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

Weight of the body at equator =  35 of initial weight ∴g′=35g (because mass remains constant)g′=g−ω2Rcos2⁡λ⇒35g=g−ω2Rcos2⁡0∘⇒ω2=2g5R⇒ω=2g5R=2×105×6400×103=7.8×10−4radsec