if a period is doubled, than the length of the pendulum should be ?

A) increased by root 2
b) quartered
c) quadrupled
d) halved
e) doubled

c) quadrupled

The period of a pendulum is the time it takes for one complete back-and-forth swing. The period is directly related to the length of the pendulum.

To determine how the length of the pendulum changes when the period is doubled, we can use the equation for the period of a pendulum:

T = 2π√(L/g)

In this equation, T represents the period, L represents the length of the pendulum, and g represents the acceleration due to gravity.

If we want to double the period (T), we can substitute 2T for T in the equation:

2T = 2π√(L/g)

Dividing both sides of the equation by 2, we get:

T = π√(L/g)

Comparing this equation to the original equation for the period, we can see that the only change is that the 2π term on the right side is now π. The square root term, which represents the length (L), remains unchanged.

Therefore, the length of the pendulum (L) remains the same when the period is doubled. So, the correct answer is:

e) doubled

The length of the pendulum should be doubled if the period is doubled.