AaßbCcDdEe AaßbCcDd Ee AaBbCcDc AaBbC No S 13) At a distance of 14,000 km from t

Question

AaßbCcDdEe AaßbCcDd Ee AaBbCcDc AaBbC No S 13) At a distance of 14,000 km from the center of Planet Z.-99, the acceleration due to gravity is 32 m/s2, What is the acceleration due to gravity at a point 28,000 km from the center of this planet? A) 8.0 m/s2 B) 16 m/s2 C) 128 m/s2 D) 4.0 m/s2 E) 2.0 m/s 14) The planet Jupiter is 7.78 × 1011 m from the sun. How long does it take for Jupiter to orbit once about the sun given that the distance from the earth to the sun is 1.50 x 1011m? A) 2.3 years B) 5.2 ycars C) 6.0 years D) 12 years E) 27 years 15) It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiters orbit is truly circular, what is the distance from Jupiter to the sun, given that the distance from the carth to the sun is 1.5 x 1011 m? A) 3.9 x 10l B)52×1011m C) 7.9 x 101llm D) 9.7 x 10ll m E)3.2 x 1012 m

Explanation / Answer

13) acceleration due to gravity g is proportional to 1/r^2.

So if r is doubled, g becomes 1/4th.

Option A is correct.

14) T = 2pi sqrt(r^3 /GM)

T = sqrt((7.78/1.5)^3) times that of earth

= 11.8 years

Option d is correct

15) again T =2pi sqrt (r^3/GM)

Using proportionality with earth,

12/1 = sqrt((r/1.5e11) ^3)

144 = (r/1.5e11)^3

r = 1.5e11 * 144^(1/3)

= 7.86e11 m

Option c is correct

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