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Quantitative Reasoning – Passage Based – Mass and Weight!

2014_QNR 24. Directions : (Questions i to iv). Read the following passage and answer the questions that follow :
Many people consider mass and weight as one and the same physical quantity though these are not Same. The quantity of matter in an object makes its mass. Its value remains the same to whichever place on Earth or even to a different heavenly body it is taken, It is also the measure of another property of a body called inertia. More is the
mass of a body, greater is its inertia/Inertia is actually the property or tendency of the body due to which it continues to be in its own state of rest or of uniform motion until an external force changes this state.
On the other hand, weight of a body is the measure of force experienced by it due to force of gravity. Its precise value varies when the body is taken from one place on Earth to another or to a different heavenly body. This happens due to change in the force of gravity at different places. The force of gravity may increase or decrease depending upon the location of the new place. Otherwise, weight and mass are directly proportional to each other. Greater is the mass of a body, greater is its weight. While mass is measured in kilogram (kg), weight is measured in a unit called Newton (N). An object of mass 1 kg on Earth weighs 9.8 N and similarly another object of mass 2 kg  Weighs 19.6 N. Weight of any other object varies exactly by the same factor. Also, the weight of an object, on Moon is about 1/6 of its weight on Earth.
(i) A body of mass m kg on Earth is taken to Moon. As compared to Earth, on Moon, its
(a) inertia will remain the same whereas weight will change.
(b) weight as well as inertia will change.
(c) weight as well as inertia will remain the same.
(d) weight will remain the same whereas inertia will change.

(ii) Which one of the following graphs shows the correct proportionality between mass
and weight of a body ?

2014_QNR 24_1

(a) A

(b) B

(c) C

(d) D

(iii) A science fiction movie was shown to students of class VIII. In the movie, two aliens XIGO and LIXO came on Earth from two different planets. XIGO weighs 245 N while LIXO weighs 392 N on Earth. However, on their own planets XIGO weighs 49 N and LIXO weighs 196 N. From this information, students concluded the following :
(i) Mass of LIXO is more than that of XIGO.
(ii) Force of gravity on a given mass on LIXO’s planet is less than that on Earth.
(iii) Force of gravity on a given mass will be more on XIGO’s planet than that on Earth and LIXO’s planet.

Which one of the following is the about the students’ conclusions ?
(a) Conclusions (i) and (ii) are correct, conclusion (iii) is not correct.
(b) Conclusions (ii) and (iii) are correct, conclusion (i) is not correct.
(c) Conclusions (i) and (iii) are correct, conclusion (ii) is not correct.
(d) All conclusions (i), (ii) and (iii) are correct.

(iv) Given below is a bar graph showing the weigh! of an object on different planets and Moon :

2014_QNR 24_2

Which of the following is correct in accordance with this bar graph for another object of weight 60 N on the surface of Moon ?
(a) Its weight on the surface of Mars will be 40.4 N.
(b) Its weight on the surface of Mercury will be 185.4 N.
(c) Its weight on the surface of Venus will be 365.7 N.
(d) Its weight on the surface of Jupiter will be 850.2 N.

Ans:

(i)  It is given in the passage that inertia (or mass) will not change. Also it is given that, the weight of an object, on Moon is about 1/6 of its weight on Earth. Hence, option (a) is correct.

(ii) If mass is zero, weight will also be. Hence option (b) is correct.

(iii) XIGO weighs  while LIXO weighs 392 N on Earth. However, on their own planets XIGO weighs 49 N and LIXO weighs 196 N.

Weight of XIGO on its own planet=49 N

Weight of XIGO on earth=245 N

Hence, force of gravity on a given mass will be less on XIGO’s planet. Conclusion (iii) is wrong.

Now, weight of LIXO on its own planet=196 N

Weight of LIXO on earth=392 N; thus, force of gravity on a given mass on LIXO’s planet is less than that on Earth. Conclusion (ii) is correct. No, need to check the first conclusion as only Option (a) fits in.

(iv) Let us look at each of the options:
(a) An object that weights 7N on the surface of Moon, weighs 15.8 on Mars. Little more than 2 times.
The object weighing 60 N on the Moon should weigh greater than 120 N. This option is wrong.

(b)An object that weights 7N on the surface of Moon, weighs 15.8 on Mercury. Little more than 2 times.
The object weighing 60 N on the Moon should weigh greater than 120 N. This option seems wrong as the values i greater than 3 times.

(c)An object that weights 7N on the surface of Moon, weighs 38. Little less than 5.5 times.
The object weighing 60 N on the Moon should weigh little less than 330 (=60*5.5) N. This option is wrong.

(d) An object that weights 7N on the surface of Moon, weighs 99.2. Little more than 14 times.
The object weighing 60 N on the Moon should weigh greater than 14*60= 840 N. This option is correct.

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