Question

find the dimensions of the quantity q from the expression T =2pie square root ml3/3Yq where T is the time period of a bar of length l mass m and youngs modulus Y

Answer 1

Answer:

Dimension of q = L^4

Explanation:

Given:

$T= 2\pi\sqrt{\frac{ml^{3} }{3Yq} }$

Now on rearranging we get

$q = 4\pi^2\frac{ml^{3} }{3YT^{2} }$

So now the dimension of q can be calculated by substituting the values of other dimension on the right.

Dimension of q = $\frac{ML^{3}}{ML^{-1}T^{-2}T^{2} }$

So we get,

Dimension of q = $L^{4}$

Answer 2

Answer:

The dimensional formula of q is $L^4$

Explanation:

• In the question we are given the formula of time period as
  $T= 2 * \pi * \sqrt{\frac{ml^3}{3Yq} }$
• Now after re arranging the above equation we get
  $q = 4\pi^2 \frac{ml^3}{3YT^2}$
• Now we can put the dimensional formula of every element present and we get the equation of q as
  $q=\frac{ML^3}{ML^-^1T^-^2T^2}\\q=L^4$
• Hence we get dimensional formula of q as
  $q=L^4$
  #SPJ2