Question

The amplitude of a damped oscillator of mass ${}^{\prime }{m}^{\prime }$ varies with the time 't' as $A=A_0{e}^{-at/m}$. The dimension of ${}^{\prime }{a}^{\prime }$ are:

• A. $M{L}^0{T}^{-1}$
• B. $M^{0}L{T}^{-1}$
• C. $M{L}^{-1}T$
• D. $ML{T}^{-1}$

Answer 1

Answer: (A)

Given, $Mass=m,time=t.A=A_0{e}^{\frac{-at}{m}}$

Since the term $\frac{-at}{m}$ is the exponential term so it is a dimension less

We know that,

The dimension of $T=\left[M^0{L}^0{T}^1\right]$ The dimension of $m=\left[M^1{L}^0{T}^0\right]$

So,

$\Rightarrow \frac{\left[a\right]\left[M^0{L}^0{T}^1\right]}{\left[M^1{L}^0{T}^0\right]}=1\Rightarrow a=\frac{\left[M^1{L}^0{T}^0\right]}{\left[M^0{L}^0{T}^1\right]}=\left[M^1{L}^0{T}^{-1}\right]$