Question

If minute is the unit of time, $10{ms}^{-2}$ is the unit of acceleration and $100kg$ is the unit of mass, then the new unit of work in $joule$ is:

• A. ${10}^6$
• B. $\frac{1}{{10}^6}$
• C. $\frac{1}{36\times {10}^6}$
• D. $36\times {10}^6$

Answer 1

The correct option is D $36\times {10}^6$

Dimensional formula of work is $M{L}^2{T}^{-2}$

Multiply and divide by $T^2$

$M{L}^2{T}^{-2}\frac{T^2}{T^2}$ $=M{L}^2{T}^{-4}{T}^2$

The term $L^2{T}^{-4}=(L{T}^{-2}{)}^2=a^2$ can be written as square of acceleration

Dimensional formula of work is same as that of $Mass\times {(acceleration\times T)}^2$

Hence, new unit of work $=100\times {(10\times 60)}^2$
$=36\times {10}^{6}J$