QuestionJune 29, 2025

A heavy stone and a light stone are released from rest in such a way that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small Which of the following statements about these stones are correct? (There could be more than one correct choice.) a) The stones must have been released from the same height. b) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. c) The initial height of the light stone is greater than the initial height of the heavy stone. d) The stones both have the same speed just as they reach the ground. e) The stones both have the same kinetic energy just as they reach the ground.

A heavy stone and a light stone are released from rest in such a way that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small Which of the following statements about these stones are correct? (There could be more than one correct choice.) a) The stones must have been released from the same height. b) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. c) The initial height of the light stone is greater than the initial height of the heavy stone. d) The stones both have the same speed just as they reach the ground. e) The stones both have the same kinetic energy just as they reach the ground.
A heavy stone and a light stone are released from rest in such a way that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small Which of the following statements about these stones are correct? (There could be more than one correct choice.) a) The stones must have been released from the same height. b) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. c) The initial height of the light stone is greater than the initial height of the heavy stone. d) The stones both have the same speed just as they reach the ground. e) The stones both have the same kinetic energy just as they reach the ground.

Solution
3.9(251 votes)

Answer

c) The initial height of the light stone is greater than the initial height of the heavy stone. ### d) The stones both have the same speed just as they reach the ground. Explanation 1. Analyze Gravitational Potential Energy Gravitational potential energy is given by **PE = mgh**. Since both stones have the same potential energy, m_{\text{heavy}}gh_{\text{heavy}} = m_{\text{light}}gh_{\text{light}}. 2. Compare Initial Heights From m_{\text{heavy}}h_{\text{heavy}} = m_{\text{light}}h_{\text{light}}, if m_{\text{heavy}} > m_{\text{light}}, then h_{\text{light}} > h_{\text{heavy}}. Thus, statement (c) is correct. 3. Analyze Speed at Ground Level Using conservation of energy, initial potential energy equals final kinetic energy: **mgh = \frac{1}{2}mv^2**. Both stones will have the same speed when reaching the ground since they started with the same potential energy. Thus, statement (d) is correct. 4. Analyze Kinetic Energy at Ground Level Since kinetic energy is **KE = \frac{1}{2}mv^2**, and both stones have the same speed but different masses, their kinetic energies will differ. Thus, statement (e) is incorrect. 5. Evaluate Other Statements Statement (a) is incorrect because different masses imply different heights for equal potential energy. Statement (b) is incorrect as both stones reach the ground with the same speed.

Explanation

1. Analyze Gravitational Potential Energy<br /> Gravitational potential energy is given by **$PE = mgh$**. Since both stones have the same potential energy, $m_{\text{heavy}}gh_{\text{heavy}} = m_{\text{light}}gh_{\text{light}}$.<br /><br />2. Compare Initial Heights<br /> From $m_{\text{heavy}}h_{\text{heavy}} = m_{\text{light}}h_{\text{light}}$, if $m_{\text{heavy}} > m_{\text{light}}$, then $h_{\text{light}} > h_{\text{heavy}}$. Thus, statement (c) is correct.<br /><br />3. Analyze Speed at Ground Level<br /> Using conservation of energy, initial potential energy equals final kinetic energy: **$mgh = \frac{1}{2}mv^2$**. Both stones will have the same speed when reaching the ground since they started with the same potential energy. Thus, statement (d) is correct.<br /><br />4. Analyze Kinetic Energy at Ground Level<br /> Since kinetic energy is **$KE = \frac{1}{2}mv^2$**, and both stones have the same speed but different masses, their kinetic energies will differ. Thus, statement (e) is incorrect.<br /><br />5. Evaluate Other Statements<br /> Statement (a) is incorrect because different masses imply different heights for equal potential energy. Statement (b) is incorrect as both stones reach the ground with the same speed.
Click to rate:

Similar Questions