Question

Two completely different planets X and Y are each composed of the same material. The planet Y has radius twice as large as that of X. The ratio of the gravitational acceleration g at the surface of Y to the gravitational acceleration g, at the surface of X is given by :

a. 1/8
b. 1/2
c. 2
d. 1/4

Answer 1

The ratio of the gravitational acceleration g at the surface of planet Y to the gravitational acceleration g at the surface of planet X is 1/4.

Step-by-step explanation:

The ratio of the gravitational acceleration g at the surface of planet Y to the gravitational acceleration g at the surface of planet X can be determined by using the formula for gravitational acceleration:

g = G * M / r²

Where:

• g is the gravitational acceleration
• G is the gravitational constant
• M is the mass of the planet
• r is the radius of the planet

Since the planets X and Y are composed of the same material, they have the same mass (M) but different radii (rX and rY). Given that the radius of planet Y is twice as large as that of planet X, we can substitute the values into the formula:

gY / gX = (G * M) / (rY²) / (G * M) / (rX²)

gY / gX = (rX / rY)²

gY / gX = (1/2)²

gY / gX = 1/4

Therefore, the ratio of the gravitational acceleration at the surface of planet Y to the gravitational acceleration at the surface of planet X is 1/4, resulting in option (d).