Question

If ${}^{\prime }m$' is the mass of a body, ${}^{\prime }{a}^{\prime }$ is amplitude of vibration, and ${}^{\prime }{w}^{\prime }$ is the angular frequency then $\frac{1}{2}{ma}^2{w}^2$ has same dimensional formula as :

• A. all the above
• B. energy
• C. moment of force
• D. work

Answer 1

Answer: (A)

Dimension of $\frac{1}{2}m{a}^2{w}^2=M{L}^2\left(\frac{1}{T^2}\right)=M{L}^2{T}^{-2}$
Work$=F.d(force\times distance)=\left(\frac{ML}{T^2}\right)\times L=M{L}^2{T}^{-2}$
Moment of force $=\underset{f}{\to }\times \underset{r}{\to }=\left[\frac{ML}{T^2}\right]\times L=M{L}^2{T}^{-2}$
Energy = work = $M{L}^2{T}^{-2}$