Physics

Velocity '$$V$$'  of a wave is directly proportional to modulus of elasticity '$$E$$' and density '$$d$$' of a medium. The expression of '$$V$$' using dimensional analysis is:


ANSWER

$$V=\sqrt { \dfrac { E }{ d } } $$


SOLUTION

$$  V\propto  E^{\alpha } d^{\beta }$$

$$M^{0}L^{1}T^{-1}=(M^{1}L^{-1}T^{-2})^{\alpha}(ML^{-3})^{\beta }$$
$$M^{0}L^{1}T^{-1}=M^{\alpha+\beta }L^{-\alpha -3\beta }T^{-2d}$$
$$\Rightarrow \alpha+\beta =0$$
$$\Rightarrow-\alpha-3\beta =1$$

$$-2\alpha=-1$$ $$ \Rightarrow \alpha =\frac{1}{2},\beta =-\frac{1}{2}$$
$$\Rightarrow v=\sqrt{\dfrac{E}{d}}$$
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Single Correct Medium Published on 18th 08, 2020
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