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Problem Questions with Answer, Solution - Exercise 10.2: Formation of Differential equations from Physical Situations | 12th Maths : UNIT 10 : Ordinary Differential Equations

Chapter: 12th Maths : UNIT 10 : Ordinary Differential Equations

Exercise 10.2: Formation of Differential equations from Physical Situations

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EXERCISE 10.2

1. Express each of the following physical statements in the form of differential equation.

(i) Radium decays at a rate proportional to the amount Q present.

(ii) The population P of a city increases at a rate proportional to the product of population and to the difference between 5,00,000 and the population.

(iii) For a certain substance, the rate of change of vapor pressure P with respect to temperature is proportional to the vapor pressure and inversely proportional to the square of the temperature.

(iv) A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuously at the rate of ₹ 400 per year.


2. Assume that a spherical rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.


Answers:

1. (i) dQ/dt = kQ (ii) dP/dt = kP(500000 − P) (iii) dP/dT = kP/T2   (iv) dx/dt = 2x/25 +400

2. dr/dt = −k

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12th Maths : UNIT 10 : Ordinary Differential Equations : Exercise 10.2: Formation of Differential equations from Physical Situations | Problem Questions with Answer, Solution

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12th Maths : UNIT 10 : Ordinary Differential Equations


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