Question

the time period of 2 simple pendleum at the place arein ratio 3:4 what will be ratio pf length​

Answer 1

Answer: The ratio of lengths will be 9 : 16.

Explanation:

We know,

time taken to complete an oscillation by a pendulum : $T = 2 \pi \sqrt{\dfrac{l}{g}}$

Therefore, 3x = 2π√L/g. (Let time = 3x & length of pendulum = L.)

=> √L/g = 3/(2π)·x

=> L/g = 9/(4π²) x²

=> L = 9/(4π²)·gx² ___(1)

Now, let the time taken by second pendulum be = 4x and length be L′.

So, 4x = 2π√L′/g

=> √L′/g = 4/(2π)·x

=> L′/g = 4/(π²)·x²

=> L′ = 4/(π²)·gx² __(2)

So, (dividing 1 with 2)

L/L′ = 9/(4π²)·gx² : 4/π²·gx²

=> Ratio of length = 9/4 : 4

=> Ratio of length = 9 : 16.

More:

You can easily calculate it in mind as:

$l \propto T^2$.