Question

The dimensional formula for amplitude of SHM is …..
$\left( a \right)\ \left[ MLT \right]$
$\left( b \right)\ \left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]$
$\left( c \right)\ \left[ {{M}^{0}}L{{T}^{0}} \right]$
$\left( d \right)\ \left[ ML{{T}^{0}} \right]$

Answer 1

Hint: We know that the dimensional formula of any term depends on the unit formula of that term in MKS dimensional unit system. Now, the amplitude means the maximum displacement of the wave. Now, by converting this into unit form we will derive the dimensional formula of amplitude in SHM.

Complete Step-by-Step solution:
As given in the question we want to derive the MLT form of amplitude in SHM. Where, M is mass, L is length and T is time.
Now, we know that the maximum displacement a wave suffers is called amplitude A, where A is distance travelled by wave.
Now, as it is the displacement of the wave it can be given by
Considering the MKS unit system, the units of x are given as:
$\text{distance x}=m$ ………………………..(ii)
Now, converting the above expressions into MLT form we get,
$x=m={{L}^{1}}$ ……………………..(iv)
Hence, the dimensional formula of amplitude is ${{M}^{0}}{{L}^{1}}{{T}^{0}}$ it can also be written as ${{M}^{0}}L{{T}^{0}}$
Thus, option(c) is correct.

Note: In such types of questions students should not get confused with MKS and CGS unit systems. If the units in the question are given in centimeter, gram or millisecond, then the student must convert into meter, kilogram and second and then derive the dimensional formula otherwise the answer will be wrong. Students should also know the dimensional formula of basic quantities such as mass, length, time etc. so that other entities can be derived or solved easily.