Question

an object is lifted from the surface of a spherical planet to an altitude equal to the radius of the planet. as a result, which of the following changes in the properties of the object take place? mass increases; weight decreases mass decreases; weight decreases mass increases; weight increases mass increases; weight remains the same mass remains the same; weight decreases mass remains the same; weight increases mass remains the same; weight remains the same

Explanation:

Step1: Define mass and weight concepts

Mass is the amount of matter in an object and is an inherent property that does not change with location. Weight \(W = mg\), where \(g\) is the acceleration due to gravity.

Step2: Recall gravitational - field formula

The acceleration due to gravity \(g\) at the surface of a planet of mass \(M\) and radius \(R\) is \(g=\frac{GM}{R^{2}}\), and at an altitude \(h = R\) (distance from the center of the planet \(r=R + h=2R\)), the acceleration due to gravity \(g'\) is \(g'=\frac{GM}{(2R)^{2}}=\frac{GM}{4R^{2}}=\frac{g}{4}\). Since \(W = mg\) and \(g\) decreases when the object is lifted to an altitude equal to the radius of the planet, the weight decreases while the mass \(m\) remains constant.

Answer:

mass remains the same; weight decreases