Question

An object has a field of g₀, with mass M0 and radius R₀. What happens to the gravitational field if the mass of the object is doubled, and the radius is tripled?

a. 2g₀/9
b. 3g₀/10
c. g₀
d. 2g₀

Answer 1

When the mass of an object is doubled and the radius is tripled, the gravitational field strength becomes 2g₀/9.

Step-by-step explanation:

To find out what happens to the gravitational field when the mass of an object is doubled and the radius is tripled, we can use the equation for gravitational field strength:

g = GM/r²

Where g is the gravitational field, G is the gravitational constant (approximately 6.67 x 10^-11 Nm²/kg²), M is the mass of the object, and r is the radius of the object.

If the mass is doubled and the radius is tripled, the equation becomes:

g' = 2GM/(3R)²

This simplifies to:

g' = (2/9)g

So, the gravitational field strength would be 2g₀/9.