Free fall: On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is
A) g/4.
B) g/2.
C) g/ .
D) g .
E) 2g.

Question

Free fall: On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is
A) g/4. 
B) g/2. 
C) g/ . 
D) g . 
E) 2g.

Quizplus · Accepted Answer

The time T it takes for the stone to return to the astronaut's hand is the time it takes for it to complete one full cycle of motion, up and then down. This means that the time it spends going up is equal to the time it spends going down.
On Earth, the stone experiences an acceleration due to gravity of g, and so its velocity changes by -gT during the upward phase, and by +gT during the downward phase.
On planet X, the stone experiences an acceleration due to gravity of gx times g (where gx is a factor we need to determine), and so its velocity changes by -gxgT during the upward phase, and by +gxgT during the downward phase.
Since the stone has the same initial velocity in both cases, we can write:
-gT = -gxgT/2    (for the upward phase)
+gT = +gxgT/2    (for the downward phase)
Simplifying these equations, we get:
gx = 2   (for planet X)
So the acceleration due to gravity on planet X is 2g, or twice the acceleration due to gravity on Earth. Therefore, the correct answer is B (g/2).

Free Fall: on the Earth, When an Astronaut Throws a 0.250-Kg