Question

The $kg\dfrac{m}{{{s^2}}}$ is the unit of
A. Momentum
B. Velocity
C. Force
D. Acceleration

Answer 1

Hint: In the given question, we have to find the physical quantity which has its unit equal to kilograms meters per seconds squared out of the options given to us. So, we find the units of all the physical quantities listed in the options one by one using some physical relations like ${\text{Momentum = }}\left( {{\text{Mass}}} \right) \times \left( {{\text{velocity}}} \right)$, ${\text{Force = }}\left( {{\text{Mass}}} \right)\times \left( {{\text{Acceleration}}} \right)$ and ${\text{Velocity = }}\dfrac{{{\text{Displacement}}}}{{{\text{Time}}}}$.

Complete step by step answer:
So, we have the unit $kg\dfrac{m}{{{s^2}}}$. We will find the physical quantity corresponding to the unit by analyzing the options. So, in option (A), we have Momentum. We know that momentum is defined as the product of mass and velocity. So, we have formula for momentum as ${\text{Momentum = }}\left( {{\text{Mass}}} \right) \times \left( {{\text{velocity}}} \right)$. Now, we know that the SI unit for mass is kilograms and velocity is meters per second. So, we get the unit for momentum as $kg\dfrac{m}{s}$.

Similarly, in option (B), we have velocity. We know that velocity is defined as displacement per unit time. So, we have formula for momentum as \[{\text{Velocity = }}\dfrac{{{\text{Displacement}}}}{{{\text{Time}}}}\]. Now, we know that the SI unit for displacement is meters and SI unit for time is seconds. So, we get the unit for velocity as $\dfrac{m}{s}$.

In option (C), we have Force. We know the force is defined as the change in momentum per unit time. So, \[{\text{Force = }}\dfrac{{{\text{Change in Momentum}}}}{{{\text{Time}}}}\]. We know that the unit of momentum is $kg\dfrac{m}{s}$ and the SI unit of time is seconds. So, we get the unit of force as $kg\dfrac{m}{{{s^2}}}$.

Now, in option (D), we have acceleration. We know that acceleration is defined as the change in velocity per unit time. So, we have, \[{\text{Acceleration = }}\dfrac{{{\text{Change in velocity}}}}{{{\text{Time}}}}\]. We know that the unit for velocity is $\dfrac{m}{s}$. Hence, the unit for acceleration is $\dfrac{m}{{{s^2}}}$.

Therefore, $kg\dfrac{m}{{{s^2}}}$ is the unit of Force.

Note: Whenever we are asked such questions related to units and physical quantities, we first write the formula relating the physical quantities involved. Then, we put the SI units of the quantities and get the units for the derived physical quantity. We must be careful while doing the calculations and should remember the formulae correctly. One should also know the laws of exponents so as to match the options and get to the required answer.