a simple pendulum complete 20 oscillations in 25 seconds the time is measured with a stopwatch of at least 0.1 least count the error in the measurement at time is
Answers
Final. Answer :Maximum percentage error in time taken., = 0.8%
Steps :
1) Least count ,
\Delta t =\frac{1}{5}=0.2sΔt=
5
1
=0.2s
Time taken to complete 20 oscillations, T = 25 s
No. of Oscillations , N = 20
Percentage error in measurement of time ,
\frac{\Delta T}{T}*100\% =?
T
ΔT
∗100%=?
We shall find relative error,
\begin{gathered}T = \frac{t}{N}\\ \\=> ln(T) = ln(\frac{t}{N})\\ \\=> ln(T) = ln(t)-ln(N) \\ \\=>\frac{\Delta T}{T}=\frac{\Delta t}{t}+0\end{gathered}
T=
N
t
=>ln(T)=ln(
N
t
)
=>ln(T)=ln(t)−ln(N)
=>
T
ΔT
=
t
Δt
+0
We get ,
\begin{gathered}T=\frac{t}{N}\\ \\=\frac{\Delta T}{T}=\frac{\Delta t}{t}\\ \\=\frac{\Delta T}{T}*100 \%\\ \\ =\frac{\Delta t}{t}*100 \%\\ \\ = \frac{0.2}{25}*100 = 0.8\%\end{gathered}
T=
N
t
=
T
ΔT
=
t
Δt
=
T
ΔT
∗100%
=
t
Δt
∗100%
=
25
0.2
∗100=0.8%
Explanation:
20 times i think
hope it help you