Question

If the length of second pendulum becomes four times, then its time period will become,
A. Four times
B. Eight times
C. Two times
D. Same as before

Answer 1

Hint: Equation of time period of oscillation of a pendulum will be helpful in finding this.
$T=2\pi \sqrt{\dfrac{l}{g}}$
Where T is the time period of oscillation, l is the length of the wire used in pendulum and g is the acceleration due to gravity. Using this equation derive the proportionality relation between the factors and find the answer.

Complete step by step answer:
First of all let us take a look at what a second’s pendulum is. It is a pendulum whose time period of oscillations is accurately two seconds. It takes one second to swing forward and another one second to swing backwards. Now let us discuss the term time period. It is the time taken to oscillate one full oscillation of a pendulum or a wave or to complete one full cycle of wave oscillation.it is given by the formula,
$T=2\pi \sqrt{\dfrac{l}{g}}$
Where T is the time period of oscillation, l is the length of the wire used in pendulum and g is the acceleration due to gravity. Using this equation we can find the relation between time taken for the oscillation and the length of the pendulum. Here as we know g is the acceleration due to gravity which is constant all over the earth. $2\pi $is also a constant. Therefore we can say that time period is directly proportional to square root of length of the pendulum. Therefore as the length of the pendulum becomes four times, the time period becomes the 2 times.

Hence, the answer for this question is option C.

Note: If the length of string increases, the pendulum falls farther than now and therefore the period of oscillation will be longer. Also as the amplitude or angle increases, farther the pendulum falls and hence longer will be the period of motion.