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Class 9Class 10First YearSecond Year
The wavelength \lambda of a wave depends on the speed v of the wave and its frequency f .Knowing that [\lambda]=[L][v]=\left[L T^{-1}\right] and [f]=\left[T^{-1}\right] Decide which of the following is correct f=v \lambda or f=v / \lambda

Name several repetitive phenomenon occurring in nature which could serve as reasonable time standard.

EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity \eta in the relation of Stokes law for the drag force F for a spherical object of radius r moving with velocity v given as F=6 \pi \eta rv.

What are the dimensions and units of gravitational constant G in the formula?$F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}$

(b) How many nanoseconds in 1 year?

Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

EXAMPLE 1.4Check the correctness of the relation v=\sqrt{\frac{F \times l}{m}} where V is the speed of transverse wave on a stretched string of tension \mathrm{F} length l and mass \mathrm{m} .