JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Gravitation

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A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take

g = 10 ms^{- 2}

at the north pole and the radius of the earth

= 6400 km

)

(A)194.66 N
(B)194.32 N
(C)195.32 N✓ Correct
(D)195.66 N

Answer: (C)

Solution

A spring balance reads the effective weight, and at the equator the earth's spin shaves a little off it through the centripetal term

m ω^{2} R

. The mass is

m = \frac{196}{10} = 19.6

kg, the angular speed is

ω = \frac{2 π}{86400}

rad/s for one turn a day, and

R = 6.4 \times 1 0^{6}

m. That rotational correction works out to about

19.6 \times (\frac{2 π}{86400})^{2} \times 6.4 \times 1 0^{6} \approx 0.67

N, so the balance now reads

196 - 0.67 \approx 195.3

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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