Question

The length of a simple pendulum is increased by 44%. The percentage change in its time period is ______.

Options

• 10%

• 20%

• 40%

• 44%

Answer 1

The length of a simple pendulum is increased by 44%. The percentage change in its time period is 20%.

Explanation:

We need to use the formula for the time period of a simple pendulum:

T = `2pisqrt(L/g)`

where: 

T is the time period,

L is the length of the pendulum,

g is the acceleration due to gravity.

Original Length = L

New Length = L′ = L + 44% of L = 1.44L

New time period becomes:

T' = `2pisqrt((1.44L)/g)`

= `2pisqrt1.44 * sqrt(L/g)`

= `sqrt1.44 * T`

`sqrt1.44 = 1.2`

⇒ T′ = 1.2T

Percentage Increase in Time Period:

`(T^' - T)/T xx 100`

= `(1.2T - T)/T xx 100`

= 0.2 × 100 = 20%