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Q.

You buy a bag of sugar of weight $W$ at a place on the equator. You take this bag to Antarctica (near the poles). In Antarctica, its weight will

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a

Does not change

b

Increase

c

Becrease

d

Vanish

answer is B.

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Detailed Solution

You buy a bag of sugar of weight

W

at a place on the equator. You take this bag to Antarctica (near the poles). In Antarctica, its weight will increase.
The weight of a body at a place depends on the gravitational acceleration

(g)

at that place. Mathematically, gravitational acceleration on Earth is represented as

g = \frac{GM}{R^{2}}

Where,

G = Gravitational constant

M = Mass of Earth

r = Radius of Earth

Since Earth is not a perfect sphere, its radius is not constant. The radius at the poles is less than that at the equator. Therefore, by equation of gravitational acceleration on Earth,

g at equator (g_{e})

is less than

g at poles (g_{p})

. As weight

(W)

is the measure of gravitational force, it is a product of mass

(m)

and acceleration due to gravity

(g)

. Therefore,

W = m \times g

. As

g_{p} > g_{e}

,

W_{p} > W_{e}

. Thus, if a bag of sugar weighs W at a certain place on the equator is taken to Antarctica, then it will weigh more due to the larger value of

g

.

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