If the radius of the Earth is doubled, what will be the change in gravitational
Practice Questions
Q1
If the radius of the Earth is doubled, what will be the change in gravitational acceleration at its surface?
It will double
It will remain the same
It will be halved
It will increase by 4 times
Questions & Step-by-Step Solutions
If the radius of the Earth is doubled, what will be the change in gravitational acceleration at its surface?
Step 1: Understand the formula for gravitational acceleration, which is g = G * M / R², where g is gravitational acceleration, G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
Step 2: Identify what happens when the radius (R) is doubled. If R is doubled, we replace R with 2R in the formula.
Step 3: Substitute 2R into the formula: g = G * M / (2R)².
Step 4: Simplify the equation: (2R)² = 4R², so g = G * M / 4R².
Step 5: Compare the new gravitational acceleration with the original: g = (G * M / R²) / 4, which means the new g is g/4.
Step 6: Conclude that if the radius of the Earth is doubled, the gravitational acceleration at its surface becomes one-fourth of its original value.
Gravitational Acceleration – The formula for gravitational acceleration at the surface of a planet is derived from Newton's law of universal gravitation, where g = G * M / R², with G being the gravitational constant, M the mass of the planet, and R the radius.
Effect of Radius on Gravitational Acceleration – Doubling the radius of the Earth affects gravitational acceleration inversely with the square of the radius, leading to a decrease in g.
