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Time period of oscillation of pendulum depends on the mass of the bog, length of the pendulum and Acceleration due to gravity. Obtain the relation between them using dimensional analysis. _________________________Please answer the above question. Best of luck ❤️Don't spam ✖️ |
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Answer» Explanation: Let Time period =T Mass of the bob = m Acceleration DUE to gravity = g Length of string = L Let T \alpha m ^{a}g ^{b}L ^{c} [T] \alpha [m] ^{a}[g] ^{b}[L] ^{c} M^{0}L^{0}T^{1}=M^{a}L^{b}T^{-2B}L^{c} M^{0}L^{0}T^{1}=M^{a}L^{b+c}T^{-2b} ⇒a=0 ⇒ Time period of oscillation is independent of mass of the bob -2b=1 ⇒b=-\frac{1}{2} b+c = 0 -\frac{1}{2} + c =0 c=\frac{1}{2} GIVING values to a,b and c in first equation T \alpha m ^{0}g ^{- \frac{1}{2} }L ^{ \frac{1}{2} } T \alpha \SQRT{ \frac{L}{g} } The real expression for Time period is T =2 \pi \sqrt{ \frac{L}{g} } Therefore time period of oscillation depends only on gravity and length of the string. Not on mass of the bob. |
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