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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 T 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**

Tags : Problem Questions with Answer, Solution , 12th Maths : UNIT 10 : Ordinary Differential Equations

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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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