Question

Plz Solve This Question With Proper Explanation!​

Answer 1

Question:

If the length of a simple pendulum is halved and mass is doubled then it's time period.

a) Increases by $\sqrt{2}$

b) Remains constant

c) Cannot be predicted

d) Decreases by $\sqrt{2}$

Answer:

$\bigstar$ Given:

→ length of a simple pendulum is halved

→ mass of a simple pendulum is doubled

$\bigstar$ To Find:

→ Time Period $T\:'$

$\bigstar$ Solution:

Time period of a Simple pendulum is given by the formula

$\boxed{{T = 2\pi\sqrt{\dfrac{l}{g} }}}$

According to the question,

$\star\;\;l \implies l/2$

$\star\;\;m \implies 2m$

Let us take the new Time period as $T\:'$

Important Point to remember,

The time period of a simple pendulum does not depend on the mass of the bob. So even if the mass of the bob gets doubled, the time period remains the same.

Therefore,

$\boxed{{T\:' = 2\pi\sqrt{\dfrac{(l/2)}{g} }}}$

$\because \;l \implies l/2$

$\implies T\:' = 2\pi\sqrt{\dfrac{l}{2g}}$

$\implies T\:' = 2\pi\sqrt{\dfrac{l}{g}}\;*\dfrac{1}{\sqrt{2} }$

We Know That,

${T = 2\pi\sqrt{\dfrac{l}{g} }}$

Therefore, after substitution

We get,

$\boxed{T\:' = \dfrac{T}{\sqrt{2} }}$

$\bigstar$ As the new time period $T\:'$ is $1/\sqrt{2}$ times the initial time period $T$

Hence, The correct option is

Option (d)

The Time Period Decreases by $\sqrt{2}$