Question

For the weight of body of mass 5 kg to be zero on equator of the earth, angular velocity of the earth must be (The radius of earth = 6400 km, acceleration due to gravity = 10 m/s²).

Options

• `1/800`rad/s

• `1/400`rad/s

• `1/80`rad/s

• `1/1600`rad/s

Answer 1

`1/800`rad/s

Explanation:

mg = `"mv"^2/"r" = "mr"omega^2`

`omega^2 = "g"/"r" = 10/(6400 xx 10^3)`

`= 10/64 xx 10^-5 = 10^-4/64`

`omega = 10^-2/8 = 1/800`rad/sec