Calculate angular velocity of earth so that acceleration due to gravity at 60° latitude becomes zero. (Radius of earth = 6400 km, gravitational acceleration at poles = 2 s 10 m , cos 60° = 0.5)

Question

Calculate angular velocity of earth so that acceleration due to gravity at 60° latitude becomes zero. (Radius of earth = 6400 km, gravitational acceleration at poles = 2 s 10 m , cos 60° = 0.5) (A) 7.8×10-2 rad/s (B) 0.5 ×10-3 rad/s (C) 1 ×10-3 rad/s (D) 2.5 × 10-3 rad/s

Tardigrade Admin · Accepted Answer

New acceleration due to gravity g' is given by g'=g-Re ω2 cos 2 λ 0 =10-6.4 × 106 ω2 cos 2 60° ⇒ ω2 =(10/6.4 × 106[0.5]2)=2.5 × 10-3 rad / s

Q. Calculate angular velocity of earth so that acceleration due to gravity at $6 0^{\circ}$ latitude becomes zero. (Radius of earth $= 6400 km$ , gravitational acceleration at poles $= 2 s 10 m$ , $cos 6 0^{\circ} = 0.5$ )

$7.8 \times 1 0^{- 2} r a d / s$

$0.5 \times 1 0^{- 3} r a d / s$

$1 \times 1 0^{- 3} r a d / s$

$2.5 \times 1 0^{- 3} r a d / s$

New acceleration due to gravity $g^{'}$ is given by
$g^{'} = g - R_{e} ω^{2} cos^{2} λ$
$0 = 10 - 6.4 \times 1 0^{6} ω^{2} cos^{2} 6 0^{\circ}$
$\Rightarrow ω^{2} = \frac{10}{6.4 \times 1 0 ^{6} [ 0.5 ] ^{2}} = 2.5 \times 1 0^{- 3} r a d / s$

Q. Calculate angular velocity of earth so that acceleration due to gravity at 60∘ latitude becomes zero. (Radius of earth =6400km, gravitational acceleration at poles =2s10m , cos60∘=0.5)

7.8×10−2rad/s

0.5×10−3rad/s

1×10−3rad/s

2.5×10−3rad/s