Gravitation

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What is the relationship between the equatorial radius and the polar radius of the Earth?

The equatorial radius is equal to the polar radius

The equatorial radius is about 21 km longer than the polar radius (correct)

The equatorial radius is about 42 km longer than the polar radius

The equatorial radius is about 21 km shorter than the polar radius

What happens to the weight of a body as it is taken from the equator to the pole?

It increases (correct)

It decreases

It becomes zero

It remains the same

At which latitude is the force of gravity least?

At 60° latitude

At the equator (correct)

At the poles

At 45° latitude

What is the relationship between the acceleration due to gravity and the height above the Earth's surface?

The acceleration due to gravity decreases with height Signup and view all the answers

What is the value of g at infinite distance from the Earth?

g is zero Signup and view all the answers

What is the acceleration due to gravity at a depth of 100 km below the Earth's surface, assuming the Earth is a sphere of uniform density?

9.66 m/s² Signup and view all the answers

At what depth would the acceleration due to gravity be 1/n times the value at the surface?

R(n-1)/n Signup and view all the answers

What is the reason for the variation in the acceleration due to gravity with latitude?

Centrifugal force due to the Earth's rotation Signup and view all the answers

What is the effect of the Earth's rotation on the weight of a body on its surface?

It decreases the weight of the body Signup and view all the answers

What is the assumption made in the calculation of the acceleration due to gravity at a certain depth?

The Earth is a sphere of uniform density Signup and view all the answers

What is the acceleration due to gravity at a height h above the surface of the Earth, if g is the acceleration due to gravity at the surface of the Earth?

g/(1 + h/R) Signup and view all the answers

What is the fractional decrease in the acceleration due to gravity at a height h above the surface of the Earth?

2h/R Signup and view all the answers

If the radius of the Earth is R, what is the height at which the acceleration due to gravity becomes 1% of its value at the surface of the Earth?

9R Signup and view all the answers

What is the weight of an object at a height h above the surface of the Earth, if W is its weight at the surface of the Earth?

W/(1 + h/R) Signup and view all the answers

What is the acceleration due to gravity at a distance 2R from the surface of the Earth, if g is the acceleration due to gravity at the surface of the Earth?

g/9 Signup and view all the answers

What is the effect of the Earth's rotation on the gravitational force at the equator?

It decreases the gravitational force Signup and view all the answers

What is the relationship between the gravitational force at the poles and the equator?

g_pole > g_equator Signup and view all the answers

What is the apparent weight of an object at the equator compared to its weight at the poles?

It is less at the equator Signup and view all the answers

What is the expression for g' at a height h above the Earth's surface?

g' = g(R^2/(R + h)^2) Signup and view all the answers

What is the gravitational force at a height h above the Earth's surface compared to its value at the surface?

It decreases with height Signup and view all the answers

At which latitude is the centrifugal force maximum?

0° Signup and view all the answers

What is the expression for the apparent weight of a body of mass m at latitude λ?

m(g - ω²R cos² λ) Signup and view all the answers

What is the value of g at the poles?

g Signup and view all the answers

By how much does the weight of a body increase when moved from the equator to the poles?

m ω²R Signup and view all the answers

What is the expression for the acceleration due to gravity at a latitude λ?

g - ω²R cos² λ Signup and view all the answers

What is the rate of decrease in acceleration due to gravity with height?

h/R^2 Signup and view all the answers

At what height does the acceleration due to gravity become 1/9 of its value at the surface of the Earth?

10R Signup and view all the answers

What is the fractional decrease in acceleration due to gravity at a height h?