Question

Two pendulum having length 16 cm and 10 cm are suspended from a rigid support. which one will having more time period and why?

plz answer it's urgent​

Answer 1

Question :

Two pendulum having length 16 cm and 10 cm are suspended from a rigid support. which one will having more time period and why?

Solution :

Two pendulum having length 16cm and 10cm are suspended from a rigid support

Time Period of a Pendulum

$\sf{T = 2\pi \sqrt{ \dfrac{L}{g} } }$

Eliminating the constants from the equation,we write :

$\implies \: \boxed{ \boxed{ \sf{T \propto \: \sqrt{L} }}}$

Thus,the time period of a pendulum is directly proportional to square root of its length

Thus,the pendulum having more length would take more time to complete one oscillation (Time Period)

$\rule{300}{2}$

One other way is to substitute the values and obtain the value

$\rule{300}{2}$

The 16cm pendulum will have more time period

Answer 2

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We are given two pendulum with length 16 cm and 10 cm respectively.

We have formula for Time period of pendulum :

$\large \star {\boxed{\sf{T \: = \: 2 \pi \sqrt{\dfrac{l}{g}}}}}$

Where,

• l is length of pendulum.
• g is gravitational force

For pendulum of length 16 cm

$\implies {\sf{T \: = \: 2 \pi \sqrt{\dfrac{16}{10}}}} \\ \\ \implies {\sf{T \: = \: 2 \pi \sqrt{1.6}}} \\ \\ \implies {\sf{T \: = \: 2 \pi 1.26}} \\ \\ \implies {\sf{T \: = \: 2.52 \pi \: s}}$

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Now for Pendulum of length 10 cm

$\implies {\sf{T \: = \: 2 \pi \sqrt{\dfrac{10}{10}}}} \\ \\ \implies {\sf{T \: = \: 2 \pi \sqrt{1}}} \\ \\ \implies {\sf{T \: = \: 2 \pi \: s}}$

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$\therefore$ Pendulum with length 16 cm will take more time