# Power delivered by a force is given by relation P = (alpha/beta)e^-beta × t. t = time. Find dimensional formula for alpha and beta.

Dear Student,

Please find below the solution to the asked query:

Here, the given relation is,

$P=\left(\frac{\alpha}{\beta}\right){e}^{-\beta t}$

Here, in exponent, the term should be unit less. Therefore,

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

And, the ratio of alpha and beta should have the dimensions of power. Therefore,

$\left[\frac{\alpha}{\beta}\right]=\left[M{L}^{2}{T}^{-3}\right]\Rightarrow \left[\alpha \right]=\left[\beta \right]\left[M{L}^{2}{T}^{-3}\right]\Rightarrow \left[\alpha \right]=\left[{M}^{0}{L}^{0}{T}^{-1}\right]\left[M{L}^{2}{T}^{-3}\right]\phantom{\rule{0ex}{0ex}}\Rightarrow \left[\alpha \right]=\left[M{L}^{2}{T}^{-4}\right]$

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

**
**