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

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 it takes for the stone to return to the astronaut's hand is given by the equation:
$$T=2\frac{v_0}{g}$$
where $v_0$ is the initial velocity and $g$ is the acceleration due to gravity. Since the initial velocity and stone are the same in both cases, we can equate the expressions for $T$ on both Earth and planet X:
$$T_{	ext{Earth}} = T_{	ext{X}} \Rightarrow 2\frac{v_0}{g_{	ext{Earth}}} = 2\frac{v_0}{g_{	ext{X}}}$$
Simplifying, we get:
$$g_{	ext{X}} = \frac{1}{2} g_{	ext{Earth}}$$
So the acceleration due to gravity on planet X is half that of Earth, which is answer choice B.

On the Earth, When an Astronaut Throws a 0