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Properties of Matter question

2017 · Shift 0 · Q61
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Properties of Matter question

2017 · Shift 0 · Q61

JEE MainPhysicsProperties of MatterMCQ+4 / −1
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :
  1. A
    181{1 \over {81}}811​
  2. B
    9
  3. C
    19{1 \over {9}}91​
  4. D
    81
View written solutionFree

Correct answer: B

  1. Use the definition of stress

Stress is

Stress=ForceArea.\text{Stress} = \frac{\text{Force}}{\text{Area}}.Stress=AreaForce​.

For the leg of the man, the force supported is essentially his weight:

F=mg.F = mg.F=mg.

So,

Stress∝mgA.\text{Stress} \propto \frac{mg}{A}.Stress∝Amg​.
  1. How mass changes when linear dimensions increase by 9

If all linear dimensions increase by a factor of 999, then volume increases by

93=729.9^3 = 729.93=729.

Since density remains the same,

m∝Volume⇒m increases by 729.m \propto \text{Volume} \Rightarrow m \text{ increases by } 729.m∝Volume⇒m increases by 729.

Hence weight mgmgmg also increases by a factor of 729729729.

  1. How area changes

The cross-sectional area of the leg is an area quantity, so it increases as the square of linear dimension:

A∝(length)2.A \propto (\text{length})^2.A∝(length)2.

Thus,

A increases by 92=81.A \text{ increases by } 9^2 = 81.A increases by 92=81.
  1. Find the factor by which stress changes

Therefore,

Stress∝72981=9.\text{Stress} \propto \frac{729}{81} = 9.Stress∝81729​=9.

So the stress in the leg increases by a factor of

9.\boxed{9}.9​.
  1. Check options
  • A: 181\frac{1}{81}811​ ❌
  • B: 999 ✅
  • C: 19\frac{1}{9}91​ ❌
  • D: 818181 ❌

Therefore, the correct option is B.

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