Question

$kgm{s^{ - 1}}$ is the SI unit of:
(A) Impulse
(B) Force
(C) Angular velocity
(D) None of these

Answer 1

Hint: To solve this question, we need to use the basic formula of each and every quantity given in the options. Then writing the SI of the quantities in the formulae, we can deduce the SI units of all the three quantities given. In this way we can eliminate all of the incorrect options.

Formula used: The formulae used for solving this question are given by
$p = mv$ where $p$ is the momentum, $m$is the mass and $v$ is the velocity.

Complete step-by-step solution:
We know that the impulse is defined as the change in momentum produced by a large force acting on a particle over a short period of time. Hence, it can be given as
$I = \Delta p$..........(1)
Now, we know that the momentum of a particle is equal to the product of its mass and velocity. So it can be written as
$p = mv$..................(2)
We know that the SI unit of the mass is kilogram $\left( {kg} \right)$, and that of the velocity is meter per second $\left( {m{s^{ - 1}}} \right)$. So from (2) the SI unit of the momentum becomes \[kgm{s^{ - 1}}\]. Since the change in a quantity has the same units as that of the quantity, so the SI unit of the change in momentum $\Delta p$ is also \[kgm{s^{ - 1}}\]. Therefore from (1) the SI unit of impulse is \[kgm{s^{ - 1}}\].
So the option A is correct.
We know from the Newton’s second law of motion that the force is equal to the rate of change of momentum, that is
$F = \dfrac{{\Delta p}}{{\Delta t}}$..............(3)
We have proved above that the SI unit of the change in momentum is \[kgm{s^{ - 1}}\]. Also we know that the SI unit of time is second. So from (3) the SI unit of the force becomes \[kgm{s^{ - 2}}\].
Therefore the option B is incorrect.
Now, we know that the angular velocity is defined as the rate of angular displacement, that is
$\omega = \dfrac{\theta }{t}$................(4)
Now, we know that the SI unit of the angular displacement is equal to radian. Also, the SI unit of time is second. So from (4) the SI unit of the angular velocity becomes radians per second, or $rad/s$.

So the option C is also incorrect.

Hence, the only correct answer is option A.

Note: There might exist more than one formula for single physical quantity. So we can choose any of the formulae to deduce the unit of the quantity according to our convenience.