the period of a simple pendulum, defined as the time necessary forone complete o

Question

the period of a simple pendulum, defined as the time necessary forone complete oscillation, is measured in time units and is given by
T = 2 pie square root of l/g
where l is the length of the pendulum and g is theacceleration due to gravity, in units of length divided by timesquared. show that this equation is dimensionally consistent. (youmight want to check the formula using your keys at the end of astring and a stopwatch)
T = 2 pie square root of l/g
where l is the length of the pendulum and g is theacceleration due to gravity, in units of length divided by timesquared. show that this equation is dimensionally consistent. (youmight want to check the formula using your keys at the end of astring and a stopwatch)

Explanation / Answer

Given time period T = 2 [ L / g] Dimensional formula of T = T Dimensional formula of L = L Dimensional formula of g = L T -2 So, Dimensional formula of [ L / g ] is =[ L / L T -2 ]                                                              = T 2                                                              = T Dimensional formula of 2 [ L / g ] =T    Since 2 have no dimensions This is equal to dimensional formula of time period . T = 2 [ L / g ] isdimensionally consistent                                                              = T Dimensional formula of 2 [ L / g ] =T    Since 2 have no dimensions This is equal to dimensional formula of time period . T = 2 [ L / g ] isdimensionally consistent

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