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Derive the equation for time period of a simple pendulum using the method of dimensions and hence obtain the equation. |
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Answer» We know that T \(\propto\) ma la gc T = K ma la gc----(1) Putting the dimension each parameter both side [T] = [M]a [L]b[LT-2]c [T] = [M]a[Lb+c][T-2c] comparing both sides power a = 0 b + c = 0 -2c = 1 c = -1/2 these value put in equation (1) we get T = K m0 l1/2 g-1/2 T = K\(\sqrt{\frac lg}\) \(\because k = 2\pi\) T = 2\(\pi\sqrt{\frac lg}\) |
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