First slide

Applications of SHM

Question

For different values of L, we get different values of $T^{2}$ . The graph between L versus $T^{2}$ is as shown in figure. Find the value of ' g ' from the given graph. Take $(π^{2} = 10)$ .

Moderate

A

$5.8 m / s^{2}$
B

$6.8 m / s^{2}$
C

$9.8 m / s^{2}$
D

$8.8 m / s^{2}$

Solution

From the equation,
$T = 2 π \sqrt{\frac{L}{g}}$
We have,
$L = (\frac{g}{4 π^{2}}) T^{2} \Rightarrow L \propto T^{2}$
i.e. L versus $T^{2}$ graph is a straight line passing through origin with slope = $\frac{g}{4 π^{2}}$
Slope = $\tan θ = \frac{g}{4 π^{2}}$ or g= $(4 π^{2}) \tan θ$
$= \frac{4 \times 10 \times 0.98}{4} = 9.8 m / s^{2}$

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