Question

The value of 60 J /min on a system which has 100 g, 100 cm and 1 min as fundamental unit is:
(A) $2.16 \times {10^6}$
(B) $2.16 \times {10^4}$
(C) $2.16 \times {10^3}$
(D) $2.16 \times {10^5}$

Answer 1

Hint: To answer this question we have to first write down the formula. We should know that each quantity has its own unit which depends upon the fundamental units of the quantities that are combined to give rise to the quantity. In this case we have to find the fundamental unit of 60 J / min. So we have to take into consideration the quantities that are measured by J and minutes and find the fundamental unit of them. This will help us to form an equation, solving which will give us an answer.

Complete step by step answer:
We should know that the fundamental units according to the given question, the system is given with 100g, 100 cm and 1 minutes. So we have to convert the units.
So we can say that let 60 joules per minute be n units.
Hence we can say that:
$
   \Rightarrow \dfrac{{{\text{60 joules}}}}{{{\text{minutes}}}}{\text{ = n}} \\
   \Rightarrow \dfrac{{{\text{60 joules}}}}{{{\text{60 seconds}}}}{\text{ = n}} \\
   \Rightarrow \dfrac{{{\text{1 joules}}}}{{{\text{second}}}}{\text{ = n}} \\
\Rightarrow \dfrac{{{\text{1 joules}}}}{{{\text{second}}}}{\text{ = 1kg}}{{\text{m}}^{\text{2}}}{\text{se}}{{\text{c}}^{{\text{ - 3}}}} \\
 $
Now we can write that:
$
  1kg{m^2}{\sec ^{ - 1}} = n(100g){(100cm)^2}{(1\min )^{ - 3}} \\
   \Rightarrow 1\left( {\dfrac{{1kg}}{{100}}} \right){\left( {\dfrac{{1m}}{{100cm}}} \right)^2}{\left( {\dfrac{{1\sec }}{{1\min }}} \right)^{ - 3}} = n \\
   \Rightarrow 1\left( {\dfrac{{1000g}}{{100}}} \right){\left( {\dfrac{{100cm}}{{100cm}}} \right)^2}{\left( {\dfrac{{1\sec }}{{60\sec }}} \right)^{ - 3}} = n \\
   \Rightarrow 1(10g){\left( {\dfrac{{1\sec }}{{60\sec }}} \right)^{ - 3}} = n \\
   \Rightarrow 1(10g){(60\sec )^3} = n \\
   \Rightarrow 10 \times 216000 = n \\
   \Rightarrow 2.16 \times {10^6} = n \\
 $
Hence we can say that the value of 60 J /min on a system which has 100 g, 100 cm and 1 min as a fundamental unit is $2.16 \times {10^6}$.

So the correct answer is option A.

Note: We should know that joule is used as a unit of work or we can use energy by the International Systems of Units (SI). When we say one joule we mean it is equal to the work done by a force which is 1 newton when it is acting through a distance of one metre.
The term fundamental units is used in the answer because it signifies that the units will not be dependent or rather be independent of each other.