Question

Calculate the values of g at Earth’s surface for the following changes in Earth’s properties: (a) its mass is doubled and its radius is halved; (b) its mass density is doubled and its radius is unchanged; (c) its mass density is halved and its mass is unchanged.

a) 4 times the original value
b) Same as the original value
c) Half the original value
d) Cannot be determined without specific values

Answer 1

To calculate the values of g at Earth’s surface for the given changes in Earth’s properties, we can use the formula for gravitational acceleration. The value of g would be 4 times the original value if the mass is doubled and the radius is halved. The value of g would be the same as the original value if the mass density is doubled and the radius is unchanged. The value of g would be half the original value if the mass density is halved and the mass is unchanged.

Step-by-step explanation:

To calculate the values of g at Earth’s surface for the given changes in Earth’s properties, we can use the formula for gravitational acceleration given by:

g = G * (M/R^2)

Where G is the gravitational constant, M is the mass of the Earth, and R is its radius. Let's calculate the values for each scenario:

a) If the mass is doubled and the radius is halved:

Using the equation, we have:

g' = (2M)/(0.5R)^2 = 4g

So, the value of g would be 4 times the original value.

b) If the mass density is doubled and the radius is unchanged:

Using the equation, we have:

g' = G * (2M/R^2) = g

So, the value of g would be the same as the original value.

c) If the mass density is halved and the mass is unchanged:

Using the equation, we have:

g' = G * (M/R^2) = 0.5g

So, the value of g would be half the original value.