Question

A simple pendulum has a wooden bob.
If the wooden bob is replaced by a
copper bob of the same size, will there
be any change in its time period?
Explain
​

Answer 1

NO, AS THE TIME PERIOD OF SIMPLE PENDULUM IS INDEPENDENT OF THE MASS OF THE BOB.

THE TIME PERIOD WILL REMAIN SAME.

Answer 2

Answer:

• The Time Period of the simple pendulum will remain Unchanged.

Explanation:

$\rule{300}{1.5}$

Time Period of a Pendulum is given by

$\qquad\boxed{\red{\tt T = 2 \; \pi \sqrt{\dfrac{l}{g}}}}$

$\mathfrak{Here}\begin{cases}\text{T Denotes Time period}\\\text{l Denotes Length of Pendulum}\\\text{g Denotes Acceleration due to gravity}\end{cases}$

So here, we can see,

$\displaystyle \dashrightarrow\tt T \propto \sqrt{l}\\\\\dashrightarrow\tt T \propto\dfrac{1}{\sqrt{g}}$

As Time period is not Proportional to the mass of the Bob of the pendulum.

Therefore,

The time period will remain unchanged if the bob is replaced from Wooden bob to copper bob as Time period is not related to mass of the bob i.e. Independent of mass of bob.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Special Cases:

1. When the length is Increased the Time period Increases as T ∝ √ (l).
2. When the length is Decreased the Time period Decreases as T ∝ √ (l).
3. When the Acceleration due to gravity  is Increased the Time period Decreases as T ∝ √ (1 / g).
4. When the Acceleration due to gravity  is Decreased the Time period Increases as T ∝ √ (1 / g).

$\rule{300}{1.5}$