A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use g =( GM / R 2)=9.8 ms -2 and radius of earth, R =6400 km .]

Question

A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use g =( GM / R 2)=9.8 ms -2 and radius of earth, R =6400 km .] (A) 49 N (B) 48.83 N (C) 49.83 N (D) 49.17 N

Tardigrade Admin · Accepted Answer

Weight of pole = mg =49 N At equator due to rotation = g e = g - R ω2 so W = mg e = m ( g - R ω2) ∴ W P > W e W P =49 N So, W e =48.83 N W e < 49 N

Q. A body weighs $49 N$ on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
(Use $g = \frac{GM}{R ^{2}} = 9.8 m s^{- 2}$ and radius of earth, $R = 6400 km .]$

$49 N$

$48.83 N$

$49.83 N$

$49.17 N$

Weight of pole $= m g = 49 N$
At equator due to rotation $= g_{e} = g - R ω^{2}$
so $W = m g_{e} = m (g - R ω^{2})$
$∴ W_{P} > W_{e} W_{P} = 49 N$
So, $W_{e} = 48.83 N W_{e} < 49 N$

Q. A body weighs 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use g=R2GM​=9.8ms−2 and radius of earth, R=6400km.]

49N

48.83N

49.83N

49.17N