Question

a simple pendulum of length l one has time period of 5 second and another simple pendulum of length l to has time period 3 second then the time period of the pendulum of length l 1 - l2 is?

Answer 1

a simple pendulum of length $l_1$ has time period of 5 second .

so, 5 = $2\pi\sqrt{\frac{l_1}{g}}$

or, 25 = 4π² × $l_1$/g

or, $l_1$ = 25g/4π² .....(1)

similarly, an another simple pendulum of length $l_2$ has time period 3 second.

so, 3 = $2\pi\sqrt{\frac{l_2}{g}}$

or, $l_2$ = 9g/4π² ......(2)

now, l = $l_1-l_2$ = 25g/4π² - 9g/4π²

= 16g/4π².....(3)

now, time period of the pendulum of length $l_1-l_2$

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

from equation (3),

T = $2\pi\sqrt{\frac{16g}{4\pi^2g}}$

= 4 second.

hence, answer is 4second.