Question

. What happens to time period of length of the pendulum is increased by four times?​

Answer 1

Time period of simple pendulum is given by

$T = 2\pi \sqrt{ \frac{l}{g} } \\ \\ T \: \: directly \: proportional \: to \: \: \sqrt{l}$

Thus if the length of pendulum is increased by 4 times, its time period gets increased by 2 times.

Answer 2

Answer:

it is given that length of a simple pendulum is increased to four times the initial length. where l is length of pendulum, T is time period and g is acceleration due to gravity. so, T ∝ √l , therefore time period of simple pendulum is directly proportional to square root of its length.

so, T √I, therefore time period of simple pendulum is directly proportional to square root of its length.

if length of simple pendulum is increased to four times.i.e., L = 4l

$so, T₁/T _2= √{l₁/1_2}$

$⇒T/T_2 = √{l/4l} = 1/2$

⇒ T_2= 2T

hence time period becomes two times of its initial.