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The time period of a pendulum depends on mass , length and acceleration due to gravity. Derive the relation among those physical quantitieSPLZ ANSWER |
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Answer» Answer: 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}Tαm a g b L c
[T] \alpha [m] ^{a}[g] ^{b}[L] ^{c}[T]α[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 T −2b L c
M^{0}L^{0}T^{1}=M^{a}L^{b+c}T^{-2b}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} 2 1
b+c = 0 -\frac{1}{2} 2 1 + c =0 c=\frac{1}{2} 2 1
Giving values to a,b and c in first equation T \alpha m ^{0}g ^{- \frac{1}{2} }L ^{ \frac{1}{2} }Tαm 0 g − 2 1
L 2 1
T \alpha \sqrt{ \frac{L}{g} }Tα g L
The real expression for Time period is T =2 \pi \sqrt{ \frac{L}{g} }T=2π g L
Therefore time period of oscillation DEPENDS only on gravity and length of the string. Not on mass of the bob. |
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