Saved Bookmarks
| 1. |
V=1÷21√T÷M find dimensions |
|
Answer» Explanation: The given relation is V=\frac{1}{2l}\sqrt{\frac{F}{m}}v= 2l 1
m F
Where, v is the frequency m is mass per unit length F is force L is length If the EQUATION is correct, the dimension on LHS should be equal to the dimensions on RHS We know that Dimensions of frequency = [T⁻¹] Dimensions of length = [L] Dimensions of Force = [MLT⁻²] Dimensions of mass per unit length = [ML⁻¹] Therefore, Dimensions of LHS in the formula = [T⁻¹] Dimensions of RHS in the formula =\frac{1}{\text{Dimension of Length}}\sqrt{\frac{\text{Dimension of Force}}{\text{Dimension of Mass per unit Length}}}= Dimension of Length 1
Dimension of Mass per unit Length Dimension of Force
=\frac{1}{[L]}\sqrt{\frac{[MLT^{-2}]}{[ML^{-1}]}}= [L] 1
[ML −1 ] [MLT −2 ]
=\frac{1}{[L]}\sqrt{L^2T^{-2}}= [L] 1
L 2 T −2
=\frac{1}{[L]}\times[LT^{-1}]= [L] 1
×[LT −1 ] =[T^{-1}]=[T −1 ] Thus, Dimensions of LHS = Dimensions of RHS Therefore, the relation is correct. Hope this answer is helpful. |
|