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
- A- 1 8
- B1 16
- C- 1 8
- 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