Question

compare the time period of simple pendulum if the ratio of length of a string is 4 :3​

Answer 1

Answer:

• The ratio of Time Period is $\underline{\sf \sqrt{4} \;\colon \sqrt{3}}$

Given:

1. The ratio of the length of the string is 4 : 3

Explanation:

$\rule{300}{1.5}$

From the formula we know,

$\displaystyle \bigstar\;\boxed{\sf T=2\;\pi\;\sqrt{\dfrac{l}{g}}}$

Where,

• T Denotes Time period

• l Denotes length of string

• g Denotes Acceleration due to gravity

From the inference we know,

$\displaystyle \dashrightarrow\sf T\propto \sqrt{l}$

Applying it for 2 cases, we get,

$\displaystyle\dashrightarrow \sf \dfrac{T_1}{T_2}=\sqrt{\dfrac{l_1}{l_2}}\\\\\\\dashrightarrow\sf \dfrac{T_1}{T_2}=\sqrt{\dfrac{4}{3}}\\\\\\\dag \quad \sf \dfrac{l_1}{l_2}=\dfrac{4}{3} \\\\\\\dashrightarrow\sf T_1\;\colon T_2=\sqrt{4}\;\colon \sqrt{3}\\\\\\\dashrightarrow \large{\underline{\boxed{\red{\sf T_1\;\colon T_2=\sqrt{4}\;\colon \sqrt{3}}}}}$

∴ The ratio of Time Period is $\underline{\sf \sqrt{4} \;\colon \sqrt{3}}$.

$\rule{300}{1.5}$

Answer 2

$\huge\underline\mathtt\red{Answer:-}$

The ratio of Time Period is $\underline{\sf \sqrt{4} \;\colon \sqrt{3}}$