Question

Q.52 :- in order to double the period of a simple pendulum, the length of the string should be

Answer 1

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Pendulum is an example for oscillator which is suspended to swing freely, when we have to double the period of oscillation of the pendulum then the length should be increased to 4 times that of the pendulum, because the period of the pendulum always depend upon length of the pendulum

When a swing moves from left side to right side to complete 1 cycle is known as period of the pendulum  

@itzunique!♥️

Answer 2

In order to double the period of a simple pendulum, the length of the string should be made 4 times the original or, quadrupled.

Given,

A simple pendulum.

To find,

To double the period, the length of the string should be?

Solution,

Firstly, let the length of the simple pendulum be $L$ and its time period be $T.$

The time period of the simple pendulum will then, be given by the relation,

$T=2\pi \sqrt{\frac{L}{g} }$     ...(1)

Now, we have to determine the variation in length if the time period is to be doubled.

Let the new length be $L'$, and the new time period be $T'.$

Substituting it in (1), we get,

$T'=2 \pi \sqrt{\frac{L'}{g} }$     ...(2)

Since the time period is to be doubled,

$\implies T'=2T$

∴ Substituting in (2) gives,

$2T=2\pi \sqrt{\frac{L'}{g} }$     ...(3)

From (1), substituting the value of $T$ in (3), we get,

$2(2\pi \sqrt{\frac{L}{g} } )=2\pi \sqrt{\frac{L'}{g} }$

Simplifying the above equation,

$2\sqrt{L} =\sqrt{L'}$

Squaring both the sides and rearranging,

$L'=4L$

⇒ The new length should be 4 times the original length.

Therefore, in order to double the period of a simple pendulum, the length of the string should be made 4 times the original or, quadrupled.

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