JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Modern Physics

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life

T

years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is

12.5%

of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of

n T

years, then the value of

n

Answer: 3

Solution

Initially, the plant produces power

P_{0}

and the village needs

0.125 P_{0} = \frac{P _{0}}{8}

. After time

t = n T

, the power available is

P = P_{0} (\frac{1}{2})^{n}

. The plant can meet the village's needs as long as

P \geq \frac{P _{0}}{8}

. At the maximum period:

P_{0} (\frac{1}{2})^{n} = \frac{P _{0}}{8} = \frac{P _{0}}{2 ^{3}}

. Therefore

n = 3

JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Integer answer

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JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Modern Physics

Solution

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