Question

Which of the following quantities has its unit as newton-second?
(A) Energy
(B) Torque
(C) Momentum
(D) Angular Momentum

Answer 1

The Newton’s second law signifies the product of force and time. We need to investigate the options by finding out the quantity whose unit can be expressed as a product of newton and second.

Formula used: In this solution we will be using the following formula;
$F = \dfrac{{\Delta p}}{t}$ where $F$ is forced and $\Delta p$ is change in momentum, $t$ is time.

Complete step by step solution:
To solve this solution, we check out each quantity for which could be a product of force and time or which quantity whose unit could be the same as the product of force and time.
First is energy, Energy in quantitative terms can be defined as the product of force and parallel distance i.e. distance in the direction of the force (this is actually work done but by the energy-work theorem, energy can be said to be that). This is force times distance and thus cannot be written as force times time. It can be eliminated from possible options.
Torque - This is the product of force and the perpendicular displacement to a centre of rotation. This too is also given by force times displacement and thus cannot be written as force times time.
Momentum – this is the product of mass and velocity. This can possibly have a unit of Newton-seconds, let’s investigate further. The unit is $kg \times m/s = kgm/s$ , now the unit of force is $N = kgm/{s^2}$ . Then newton-second would be $Ns = kg\dfrac{m}{{{s^2}}} \times s = kg\dfrac{m}{s} = kgm/s$ which is the same as momentum, hence momentum can also have a unit of newton-seconds
Thus, the correct answer is C.

Note:
Alternatively, from Newton’s second law, we have
$F = \dfrac{{\Delta p}}{t}$ where $F$ is forced and $\Delta p$ is change in momentum, $t$ is time. By cross multiplying,
$Ft = \Delta p$ . The left hand side has a unit of newton second, hence the right hand side must also have a unit of newton second.