First slide

Simple hormonic motion

Question

Statement A: The time period of a simple pendulum of infinite length is infinite.
Statement B: The time period of a simple pendulum is directly proportional to the square root of length.

Moderate

A

If both statement A and statement B are true and statement B is the correct explanation of statement I.
B

If both statement A is false. Statement B is true.
C

If statement A is true but statement B is false
D

If both statement A and statement IB are false

Solution

If length of the pendulum is large, g no longer remains vertical but will be directed towards the centre of the earth and expression of the time period is given by
T = $2 π \sqrt{\frac{1}{g (\frac{1}{l} + \frac{1}{R})}}$
Here, R is the radius of earth.
$if l \underset{}{\to} \infty$ , $\frac{1}{l} \to 0$
and $T = 2 π \sqrt{\frac{R}{g}} = 84.6 \min$
In general, time period of a simple pendulum

$T = 2 π \sqrt{\frac{l}{g}}$
or $T \propto \sqrt{l}$

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