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Suppose that the Earth's mass is doubled, but its radius remains unchanged. How will this change the escape velocity? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by v2). O The escape velocity will be halved. O The escape velocity will decrease by about 30 percent (i.e., it will be divided by 2). O The escape velocity will be unchanged. Suppose that the Earth's radius is doubled, but its mass remains unchanged (i.e. R = 1.28 x 10' m and M = 5.97 x 1024 kg). How will the escape velocity be affected? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by V2). O The escape velocity will be halved. O The escape velocity will decrease by about 30 percent (i.e., it will be divided by 2). O The escape velocity will be unchanged. Suppose that the Earth's mass and radius are both doubled (i.e. R = 1.28 x 10' m and M = 1.19 x 1025 kg). How will the escape velocity be affected? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by 2).

Suppose that the Earth's mass is doubled, but its radius remains unchanged. How will this change the escape velocity? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by v2). O The escape velocity will be halved. O The escape velocity will decrease by about 30 percent (i.e., it will be divided by 2). O The escape velocity will be unchanged. Suppose that the Earth's radius is doubled, but its mass remains unchanged (i.e. R = 1.28 x 10' m and M = 5.97 x 1024 kg). How will the escape velocity be affected? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by V2). O The escape velocity will be halved. O The escape velocity will decrease by about 30 percent (i.e., it will be divided by 2). O The escape velocity will be unchanged. Suppose that the Earth's mass and radius are both doubled (i.e. R = 1.28 x 10' m and M = 1.19 x 1025 kg). How will the escape velocity be affected? O The escape velocity will be doubled. O The escape velocity will increase by about 40 percent (i.e., it will be multiplied by 2).

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### Understanding Escape Velocity Changes in Different Scenarios #### (c) Doubling the Earth's Mass Suppose that the Earth's mass is doubled, but its radius remains unchanged. How will this change the escape velocity? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. #### (d) Doubling the Earth's Radius Suppose that the Earth's radius is doubled, but its mass remains unchanged (i.e., \( R = 1.28 \times 10^7 \) m and \( M = 5.97 \times 10^{24} \) kg). How will the escape velocity be affected? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. #### (e) Doubling Both Mass and Radius Suppose that the Earth's mass and radius are both doubled (i.e., \( R = 1.28 \times 10^7 \) m and \( M = 1.19 \times 10^{25} \) kg). How will the escape velocity be affected? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. These scenarios explore how alterations in the Earth's mass and radius affect the escape velocity, an important concept in physics related to gravitational forces and energy dynamics.
Transcribed Image Text:### Understanding Escape Velocity Changes in Different Scenarios #### (c) Doubling the Earth's Mass Suppose that the Earth's mass is doubled, but its radius remains unchanged. How will this change the escape velocity? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. #### (d) Doubling the Earth's Radius Suppose that the Earth's radius is doubled, but its mass remains unchanged (i.e., \( R = 1.28 \times 10^7 \) m and \( M = 5.97 \times 10^{24} \) kg). How will the escape velocity be affected? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. #### (e) Doubling Both Mass and Radius Suppose that the Earth's mass and radius are both doubled (i.e., \( R = 1.28 \times 10^7 \) m and \( M = 1.19 \times 10^{25} \) kg). How will the escape velocity be affected? - ○ The escape velocity will be doubled. - ○ The escape velocity will increase by about 40 percent (i.e., it will be multiplied by \( \sqrt{2} \)). - ○ The escape velocity will be halved. - ○ The escape velocity will decrease by about 30 percent (i.e., it will be divided by \( \sqrt{2} \)). - ○ The escape velocity will be unchanged. These scenarios explore how alterations in the Earth's mass and radius affect the escape velocity, an important concept in physics related to gravitational forces and energy dynamics.
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