The colonization of Mars is a favorite topic among science fiction writers. It i
ID: 1482488 • Letter: T
Question
The colonization of Mars is a favorite topic among science fiction writers. It is a smaller planet than Earth and further from the Sun. Its radius is 0.5 times that of Earth, and its mass is 0.1 times that of Earth. It is 1.5 times further from the Sun than Earth. On Earth the acceleration due to gravity is 10 m/s2.
3. If a person was standing on the surface of Mars and dropped a Martian rock, what is the approximate acceleration of the rock’s fall?
A) 0.3 m/s2
B) 1 m/s2
C) 2 m/s2
D) 4 m/s2 4.
How does the force of attraction between the Sun and Mars compare with that between the Sun and Earth?
A) 0.04 times, weaker
B) 0.07 times, weaker.
C) 0.10 times, weaker.
D) There is not enough information to answer this question.
Explanation / Answer
3) Correct ans :D) 4 m/s2
explanatoin:
Given,
r = 0.5 Re ; m = 0.1 Me ;
We know that,
g = G M /R2
g(e) = G Me /Re2
g(m) = G m /r2 = G 0.1 Me /0.25Re2
g(e)/g(m) = G Me/Re x 0.25 Re2 / G 0.1Me = 2.5
10/g(m) = 2.5 => g(m) = 10/2.5 = 4 m/s2
Hence, D) 4 m/s2
Correct ans: (A) 0.04 times, weaker
explanation:
We know that, Fgravity = G M m /R2
F(earth sun) = G Me Ms / R2
F(mars sun) = G m Ms / (1.5R)2 = G (0.1 Me) Ms / 2.25 R2
F(earth sun)/F(mars sun) = G Me Ms / R2 x 2.25 R2 / G (0.1) Me Ms = 22.5
F(mars sun) = F(earth sun)/22.5 = 0.04 F(earth sun)
hence, (A) 0.04 times, weaker