Question

The unit of force, velocity and energy are 100 dynes, $10cm{{s}^{-1}}\ and\,500$erg respectively. The units of mass, length and time are:
(A) $5\ g,\ 5\ cm,\ 5\ s$
(B) $5\ g,\ 5\ cm,\ 0.5\ s$
(C) $0.5\ g,\ 5\ cm,\ 5\ s$
(D) $5\ g,\ 0.5\ cm,\ 5\ s$

Answer 1

Hint: We know that a force is defined as any interaction that when unopposed will change the motion of an object. A force can cause an object with mass to change its velocity, that is accelerate. By velocity we mean includes to begin moving from a state of rest. A force has both magnitude and direction making it a vector quantity. Based on this concept we have to solve this question.

Complete step by step answer:
At first let us write that the force is given as, along with the dimension of force is:
$Force=100dyne={{M}^{1}}{{L}^{1}}{{T}^{-2}}$
Then now let us write that the velocity is given as, along with the dimension of velocity is:
$Velocity=10\dfrac{cm}{s}=L{{T}^{-1}}$
So finally, the formula for energy and the dimension of energy is given as:
$Energy=500erg={{M}^{1}}{{L}^{2}}{{T}^{-2}}\Rightarrow \dfrac{energy}{force}={{L}^{1}}=\dfrac{500}{100}=5cm$
Now we have to find the value of the expression as:
$\Rightarrow \dfrac{energy}{{{(velocity)}^{2}}}={{M}^{1}}=\dfrac{500}{{{(10)}^{2}}}=5gm\Rightarrow T=0.5sec$
So, we can say that the units of mass, length and time are $5\ g,\ 5\ cm,\ 0.5\ s$.

Hence, the correct answer is Option B.

Note: We know that energy is defined as the strength to do any kind of physical quantity. We can also say that energy is defined as the ability to do work. The physical or chemical resources are processed to generate energy which is further used to provide light or heat for domestic or industrial purposes.
We should also know that energy can exist in a variety of forms, such as electrical, mechanical, chemical, thermal or nuclear, and can be transformed from one form to another. It is measured in the unit of joules or watts.