A 12 kg pendulum bob attached to a string The string is pull

A 1.2 kg pendulum bob attached to a string. The string is pulled back until it forms a 18° angle with the vertical. When it is released the pendulum bob takes 1.8 seconds to complete one complete cycle.

When someone switches the 1.2 kg pendulum bob with a 2.0 kg pendulum bob, how long will it take for the pendulum bob to complete one cycle?

A 1.2 kg pendulum bob attached to a string. The string is pulled back until it forms a 18° angle with the vertical. When it is released the pendulum bob takes 1.8 seconds to complete one complete cycle.

When someone triples the lenth of the pendulum bob, how long will it take for the pendulum bob to complete one cycle?

thanks in advance :)

Solution

a)

For a pendulum,

the time period is given by :

T = 2*pi*sqrt(L/g)

As evident from the equation , the time period does not depend on the mass of the pendulum bob

So, the time period will remain same.

So, time taken for the bob to complete one cycle = 1.8 s

b)

T =  2*pi*sqrt(L/g)

So, T is proportional to sqrt(L)

So, as Length(L) is tripled,

T is sqrt(3) times = 1.73 times

So, time taken for one cycle = 1.73*1.8 = 3.11 s <------answer