The weights of three objects X, Y and Z measured on three celestial bodies are listed in the box. (g on the Moon, Jupiter and Mercury are 1.7 m s-2, 25.4 m s-2 and 3.8 m s-2 respectively)  Object X on the Moon is 340 N.  Object Y on Jupiter is 6096 N.  Object Z on Mercury is 399 N. Which of the following sequences shows X, Y, and Z in ascending order of their masses?

The weights of three objects X, Y and Z measured on three celestial bodies are listed in the box. (g on the Moon, Jupiter and Mercury are 1.7 m s-2, 25.4 m s-2 and 3.8 m s-2 respectively)  Object X on the Moon is 340 N.  Object Y on Jupiter is 6096 N.  Object Z on Mercury is 399 N. Which of the following sequences shows X, Y, and Z in ascending order of their masses? Correct Answer Z, X, Y

CONCEPT:

  • The acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by the earth
  • Weight: The force applied by the earth on anybody having mass is called the weight of that body.
    • It is denoted by W.
    • Mathematically it is can be written as

⇒ W = mg

Where m = mass of the body and g = acceleration due to gravity

EXPLANATION:

Given - gMoon = 1.7 m s-2, g= 25.4 m s-2, gMer = 3.8 m s-2, WMoon = 340 N, WJ = 6096 N and WMer = 399 N

  • The weight of the body on the moon can be calculated as

⇒ WMoon = mMoongMoon

⇒ mMoon =   WMoon/ gMoon = 340/1.7 = 200 kg      ------- (1)

  • The weight of the body on the Jupiter can be calculated as

⇒ WJupiter  = mJupitergJupiter 

⇒ mJupiter =   WJupiter/ mJupiter = 6096/25.4 = 240 kg      ------- (2)

  • The weight of the body on the mercury can be calculated as

⇒ Wmercury  = mmercurygmercury

⇒ mmercury =   Wmercury/ gmercury = 399/3.8 = 105 kg      ------- (3)

  • From the above equations, it is clear that the mass of the object is least on mercury and it is maximum on the Jupiter. 
  • Therefore, the ascending order of their masses is Z, X, Y. Hence option 2 is correct.

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