Question

The correct dimensional formula for the impulse is given by
A. \[ML{T^{ - 2}}\]
B. \[M{L^2}{T^{ - 2}}\]
C. \[ML{T^{ - 1}}\]
D. \[M{L^2}{T^{ - 1}}\]

Answer 1

Hint: First, we will write the formula for the impulse that is impulse is equal to force multiplied by time. Then we will write the formula for the force that is mass multiplied by acceleration. After that, we will put the units of mass, time, and acceleration in terms of length, time, and mass in the formula and we will get the required unit of impulse.

Complete Step-by-Step solution:
  Let us assume M= Mass
                            L= length
                            T=Time
We know ${\text{Impulse =} Force \times Time}$------------------------- (1)
And, we also know ${\text{Force =} Mass \times Acceleration}$----------------- (2)
Here ${\text{Acceleration = Length/tim}}{{\text{e}}^{\text{2}}}$--------------------------- (3)
So now we will write the formulas in terms of basic units that are length, Mass, and Time.
From equation (3) we can write \[{\text{Acceleration}} = \left[ {L/{T^2}} \right] = \left[ {L{T^{ - 2}}} \right]\]------ (4)
Substituting equation (4) in equation (2) we will get ${\text{Force}} = \left[ {ML{T^{ - 2}}} \right]$--- (5)
Finally substituting equation (5) in (1) we will get
${\text{Impulse}} = \left[ {ML{T^{ - 1}}} \right] = \left[ {{M^1}{L^1}{T^{ - 1}}} \right]$

Therefore the dimensional for Impulse is $\left[ {{M^1}{L^1}{T^{ - 1}}} \right]$that is option C.

Note: For these types of questions always try to write the given in terms of its formula then break the formula into smaller basic formulas till we get the most basic formula. Then starting from the most basic formula write its units and go on substitution the obtained unit in larger formula till you obtain the required unit.