Question

A freely falling body takes $2$ seconds to reach the ground on a planet when it is dropped from, a height of $8m$. If the period of a simple pendulum is $2$ seconds on that planet then its length is:

• A. $40cm$
• B. $50cm$
• C. $75cm$
• D. $25cm$

Answer 1

The correct option is A $40cm$

$T=2sec$

$u=0m/s$ initial velocity

$t=2sec$

$h=8m$

The time period of simple pendulum,

$T=2\pi \sqrt{\frac{l}{a}}$. . . . .(1)

2nd equation of motion,

$S=h=ut+\frac{1}{2}a{t}^2$

$8=\frac{1}{2}a\times 2\times 2$

$a=4m/s^2$

From equation (1),

$T=2\pi \sqrt{\frac{l}{a}}$

$2=2\pi \sqrt{\frac{l}{4}}$

$\frac{1}{{\pi }^2}=\frac{l}{4}$

$l=\frac{4}{(3.14{)}^2}$

$l=40cm$

The correct option is A.