Question

Two pendulums P and Q have equal lengths but their bobs weigh 10gf and 20gf
respectively. (i) Compare their time periods.
(ii) Give a reason for your answer.
Plz help

Answer 1

=> Time period of simple pendulum is given by

$t = 2\pi \sqrt{ \frac{l}{g} }$

where, l = length and g = gravitational acceleration

=> Time period depends only upon length of pendulum.

=> But here length of both pendulum is same.

=> As per formula time period is not depends upon weight of bob...

=> So, time period of both P and Q pendulum is same...

=> T1/T2 = 1

Tnx....

Answer 2

Answer:

Given:

Length of Pendulum P and Q is same.

Weight of the Bob is given as follows:

• P = 10 gf
• Q = 20 gf

To find:

Ratio of time periods

Concept:

Time period of pendulum is given as :

$t = 2\pi \sqrt{ \dfrac{l}{g} }$

As per the Equation, for a constant gravitational Acceleration, the time period is only dependent on length of Pendulum.

Calculation:

Let l1 = l2 = l (as per the question)

Time period for Pendulum P

$\therefore \: t1 = 2\pi \sqrt{ \dfrac{l1}{g} } \\ = > t1 = 2\pi \sqrt{ \dfrac{l}{g} }$

Time period for Pendulum Q:

$\therefore \: t2 = 2\pi \sqrt{ \dfrac{l2}{g} } \\ = > t2 = 2\pi \sqrt{ \dfrac{l}{g} }$

So the time period of both the pendulum is same.

$\boxed{ \red{ \therefore \: t1 = t2}}$