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AP EAMCET2013MathematicsApplication of Derivatives

The relation between pressure p and volume V is given by p V^ 1 / 4 = constant. If the percentage decrease in volume is 1 2 , then the percentage increase in pressure is

Options

  1. A- 1 8
  2. B1 16
  3. C- 1 8
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

Given, p V^ 1 / 4 =a , where a is constant. p= a V^ 1 / 4 Decreased volume aligned & =V^ 1 / 4 - V^ 1 / 4 200 = 199 200 V^ 1 / 4 & Increased pressure = a 199 200 V^ 1 / 4 = 200 a 199 V^ 1 / 4 aligned Percentage increase in pressure aligned & = 200 a 199 V^ 1 / 4 - a V^ 1 / 4 a V^ 1 / 4 100 & = ( 200 199 -1 ) 100 & = 100 199 1 2 ( approximate ) aligned

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