A wire of length 6 m is stretched such that its radius is reduced by 20%. Which one of the following is the value of increase in its length?
- A.50%
- B.56.25%
- C.62.25%
- D.75%
Correct answer
Explanation
The correct answer is B, 56.25%. When a wire is stretched its volume stays the same, so the length must grow in the same ratio as the cross-sectional area shrinks.
Volume V = πr² × L. If the radius falls by 20%, the new radius is 0.8r and the new area is 0.64 times the old area. For the volume to stay constant, the new length must be L ÷ 0.64 = 1.5625 L. For the 6 m wire that is 9.375 m, an increase of 3.375 m, or 56.25%. The same reasoning is used to find the new resistance of a stretched wire, since R = ρL ÷ A.
A is wrong because 50% assumes the length rises by 2.5 times the fall in radius, ignoring that area depends on the square of the radius. C is wrong because 62.25% does not follow from 1 ÷ 0.64 and appears to be a slip in the calculation. D is wrong because 75% would need the area to fall to about 57% of its value, a radius cut of nearly 25%.
Exam tip: stretched wire, volume constant: L₂/L₁ = (r₁/r₂)²; radius × 0.8 gives length × 1.5625.
Practice Questions
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- A.1 only
- B.2 and 3 only
- C.1 and 3 only
- D.1, 2 and 3
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- D.It is used in aircraft industry.
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- B.The sensitivity of the human ear does not vary with the frequency of the sound.
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- C.sufficient vitamins but deficient fats in diet
- D.sufficient fats but deficient vitamins in diet
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- A.Coffee < Lemon juice < Milk of magnesia < Blood
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- C.Lemon juice < Blood < Coffee < Milk of magnesia
- D.Lemon juice < Coffee < Blood < Milk of magnesia
Show answer
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