If the radius of a planet is halved while keeping its mass constant, how does th

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Question: If the radius of a planet is halved while keeping its mass constant, how does the gravitational acceleration at its surface change?

Options:

Correct Answer: It becomes four times stronger

Solution:

If the radius is halved, the gravitational acceleration becomes four times stronger, as g is inversely proportional to the square of the radius.

If the radius of a planet is halved while keeping its mass constant, how does the gravitational acceleration at its surface change?

If the radius of a planet is halved while keeping its mass constant, how does the gravitational acceleration at its surface change?

Step 1: Understand that gravitational acceleration (g) at the surface of a planet is calculated using the formula g = G * M / R^2, where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Step 2: Note that in this scenario, the mass (M) of the planet remains constant, but the radius (R) is halved. This means R becomes R/2.
Step 3: Substitute the new radius into the formula: g = G * M / (R/2)^2.
Step 4: Simplify the equation: (R/2)^2 = R^2 / 4, so g = G * M / (R^2 / 4) = G * M * 4 / R^2.
Step 5: This shows that the new gravitational acceleration is g' = 4 * (G * M / R^2), which means the gravitational acceleration is now four times stronger than before.

Gravitational Acceleration – Gravitational acceleration at the surface of a planet is determined by the formula g = G * M / r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius.
Inverse Square Law – The gravitational force (and thus acceleration) is inversely proportional to the square of the radius, meaning that if the radius decreases, the gravitational acceleration increases significantly.