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

Let's use the formula for the time it takes for an object to reach its maximum height and fall back down to its starting point:
$$T = \frac{2v_0}{g}$$
where T is the time taken, v0 is the initial velocity, and g is the acceleration due to gravity.
Since the astronaut throws the stone with the same initial velocity on both Earth and planet X, we can write:
$$\frac{T_X}{T_E} = \frac{g_E}{g_X}$$
where TX and TE are the times taken for the stone to return on planet X and Earth, respectively. Solving for gX, we get:
$$g_X = \frac{T_E}{T_X} g_E$$
Substituting the given values, we get:
$$g_X = \frac{T_E}{2T_E} g_E = \frac{1}{2} g_E$$
Therefore, the acceleration due to gravity on planet X (in terms of g) is g/2. Answer: B)

On the Earth, When an Astronaut Throws a 0