The angular speed of earth in rad/s so that the objects on equator may appear weightless (taking g=10 text m/s2 and radius of earth =6400 km) is

Question

The angular speed of earth in rad/s so that the objects on equator may appear weightless (taking g=10 text m/s2 and radius of earth =6400 km) is (A)  1.56  (B)  1.25× 10-1  (C)  1.56× 10-3  (D)  1.25× 10-3

Tardigrade Admin · Accepted Answer

: Weight of the body = Centripetal force ∴ mg=mRω 2 or ω =√g/R=√(10/6400× 103)=(1/8× 102) =1.25× 10-3rad/ sec

Q. The angular speed of earth in rad/s so that the objects on equator may appear weightless (taking $g = 10 m / s^{2}$ and radius of earth $= 6400$ km) is

$1.56$

$1.25 \times 10^{- 1}$

$1.56 \times 10^{- 3}$

$1.25 \times 10^{- 3}$

: Weight of the body = Centripetal force $∴$ $m g = m R ω^{2}$ or $ω = g / R = \frac{10}{6400 \times 10 ^{3}} = \frac{1}{8 \times 10 ^{2}}$ $= 1.25 \times 10^{- 3} r a d / sec$

Q. The angular speed of earth in rad/s so that the objects on equator may appear weightless (taking g=10m/s2 and radius of earth =6400 km) is

1.56

1.25×10−1

1.56×10−3

1.25×10−3