Question

A simple pendulum completes 30 vibrations
in 50 seconds calculate the length of the
Pendulum . Take g = 9.8 m/s²

Do it asap you will be marked the brainliest getting 47
points within 5 minutes plz answer my online class is going on

Answer 1

SoluTion :

✴ Given :-

▪ A simple pendulum completes 30 vibrations in 50 seconds.

✴ To Find :-

▪ Length of simple pendulum

✴ Concept :-

✈ Time period is defined as time requires to complete obe oscillation.

Mathematically,

$\sf{\pink{\large{Time\:Period=\dfrac{Total\:time}{no.\:of\:oscillation}}}}$

We also know that,

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

• T denotes time period
• l denotes length of pendulum
• g denotes gravitational acceleration

✴ Calculation :-

$\implies\sf\:2\pi\sqrt{\dfrac{l}{g}}=\dfrac{Total\:time}{no.\:of\:oscillation}\\ \\ \implies\sf\:2\pi\sqrt{\dfrac{l}{9.8}}=\dfrac{50}{30}\\ \\ \implies\sf\:l=\dfrac{25\times 9.8}{9\times 4{\pi}^2}\\ \\ \implies\:\boxed{\sf{\orange{\large{l=0.69 \:m}}}}$

_________________________________

✒ Length of simple pendulum = 0.69 m

Answer 2

GiveN :

• Time = 50 s
• No. of vibration = 30
• g = 9.8 m/s²

To FinD :

• Length of the Pendulum

Solution :

As we know that :

$\dashrightarrow \sf{Time \: Period \: = \: \dfrac{Time}{No. \: of \: vibration} \: \: \: \: \: ...(1)}$

And also,

$\dashrightarrow \sf{Time \: = \: 2 \pi \sqrt{\dfrac{l}{g}} \: \: \: \: \: ...(2)}$

Equate (1) and (2)

$\dashrightarrow \tt{2 \pi \sqrt{\dfrac{l}{g}} \: = \: \dfrac{Time}{No. \: of \: vibration}} \\ \\ \dashrightarrow \tt{2 \pi \sqrt{\dfrac{l}{9.8}} \: = \: \dfrac{50}{30}} \\ \\ \dashrightarrow \tt{2 \pi \sqrt{\dfrac{l}{9.8}} \: = \: \dfrac{5}{3}}$

Square Both Sides

$\dashrightarrow \tt{\bigg( 2\pi \sqrt{\dfrac{l}{9.8}} \bigg) ^2 \: = \: \bigg( \dfrac{5}{3} \bigg) ^2} \\ \\ \dashrightarrow \tt{4 \pi ^2 \dfrac{l}{9.8} \: = \: \dfrac{25}{9}} \\ \\ \dashrightarrow \tt{l \: = \: \dfrac{25 \: \times \: 9.8}{9 \: \times \: 4 \pi^2}} \\ \\ \dashrightarrow \tt{l \: = \: \dfrac{245}{355}} \\ \\ \dashrightarrow \tt{l \: = \: 0.69} \\ \\ \underline{\sf{\therefore \: length \: of \: Pendulum \: is \: 0.69 \: m}}$