First slide

Applications of SHM

Question

In a certain observation of experiment with simple pendulum we get $l = 23.2 cm$ , $r = 1.32 cm$ and time taken for 20 oscillations was $20.0 s e c$ . Taking $π^{2} = 10$ , find the value of g in proper significant figures.

Moderate

A

$4.80 m / s^{2}$
B

$9.60 m / s^{2}$
C

$8.80 m / s^{2}$
D

$9.80 m / s^{2}$

Solution

Equivalent length of pendulum,
$L = 23.2 cm + 1.32 cm = 24.52 cm$
$= 24.5 cm$ (according to addition rule of significant figures)
Time period, $T = \frac{20.0}{20} = 1.00 s$ . Time period has 3 significant figures
$g = (4 π^{2}) \frac{l}{T^{2}} = \frac{4 \times 10 \times 24.5 \times 10^{- 2}}{(1.00)^{2}} = 9.80 m / s^{2}$

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