Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{ML}^{3}}{3 \mathrm{Yq}}}$ then find the dimensions of q. Where $\mathrm{T}$ is the time period of bar of mass $\mathrm{M}$ length $\mathrm{L}$ and Young modulus $\mathrm{Y}$.
Options:
Solution:
2492 Upvotes
Verified Answer
The correct answer is:
$\left[\mathrm{L}^{4}\right]$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{ML}^{3}}{3 \mathrm{Yq}}},$ writing dimensions of both
the sides, we get $[\mathrm{T}]=\left[\frac{\mathrm{ML}^{3}}{\mathrm{ML}^{-1} \mathrm{~T}^{-2} \mathrm{q}}\right]^{1 / 2}$
or $\quad q=\left[L^{4}\right]$
the sides, we get $[\mathrm{T}]=\left[\frac{\mathrm{ML}^{3}}{\mathrm{ML}^{-1} \mathrm{~T}^{-2} \mathrm{q}}\right]^{1 / 2}$
or $\quad q=\left[L^{4}\right]$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.