Answer:
(a) T = 1.3565s (b)L = 0.4567m
Explanation:
One of the formulas of simple pendulum problem is:
[tex]T=2\pi\cdot \sqrt{\frac{L}{g}}[/tex], where T is the pendulum period, L is the pendulum length and g is the acceleration of gravity.
Question a
It must be taken into account that the period is the time the pendulum takes to make a complete oscillation. With that in mind, if the pendulum makes 115 complete oscillations in 2.60 min, the way to find the time required for an oscillation is dividing the total time spent by the total oscillations made.
Before making that operation, it is important to convert the units of the time to the International System of Units to get a proper result, it means convert minutes to seconds.
Because 1 min has 60 seconds, 2.60min has (2.60x60) seconds, which equals to 156 seconds.
Now, we can proceed with the operation.
[tex]T=\frac{156s}{115}=1.3565s[/tex]
The previous result means that an oscillations takes 1.3565s which correspond to the period.
Question b
From the formula set at the beginning, we must modify it to obtain a formula for the length (L).
It is [tex]L=g\cdot \bigg( \frac{T}{2\pi }\Big)^2[/tex]
The final step is to replace the values of T and g.
[tex]L=9.8\cdot \bigg( \frac{1.3565}{2\pi }\Big)^2=0.4567m[/tex]
The length of the pendulum is 0.4567m or 45.67cm
