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What will be the acceleration due to gravity on the surface of the moon, if its radius is 1/4th the radius of the earth and its mass is 1/80th the mass of the earth?
  • a)
    g/2
  • b)
    g/3
  • c)
    g/4
  • d)
    g/5
Correct answer is option 'D'. Can you explain this answer?
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The acceleration due to gravity on the surface of the moon can be calculated using Newton's law of universal gravitation.
- Given data:
- Radius of the moon (r_m) = Radius of the Earth (r_e) / 4
- Mass of the moon (m_m) = Mass of the Earth (m_e) / 80
- Formula for acceleration due to gravity (g) on the surface of a celestial body:
- g = G * (mass of the celestial body) / (radius of the celestial body)^2
- Substitute the given data into the formula:
- g_moon = G * m_m / r_m^2
- g_moon = G * (m_e / 80) / (r_e / 4)^2
- g_moon = G * (m_e / 80) / (r_e^2 / 16)
- g_moon = G * (m_e / 80) * (16 / r_e^2)
- g_moon = G * m_e * 16 / (80 * r_e^2)
- g_moon = G * m_e / (5 * r_e^2)
- g_moon = g_e / 5 [where g_e is the acceleration due to gravity on Earth]
Therefore, the acceleration due to gravity on the surface of the moon is 1/5th of the acceleration due to gravity on Earth. So, the correct answer is option 'd) g/5'.
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What will be the acceleration due to gravity on the surface of the moon, if its radius is 1/4th the radius of the earth and its mass is 1/80th the mass of the earth?a)g/2b)g/3c)g/4d)g/5Correct answer is option 'D'. Can you explain this answer?
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