Careers360 Logo
NEET OMR Sheet Sample 2025 PDF: NEET OMR Sheet For Practice

Oscillation Of Pendulum MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Simple pendulum is considered one the most difficult concept.

  • 38 Questions around this concept.

Solve by difficulty

A child swinging on a swing in sitting position stands up, then the time period of the swing will :

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

What should come in place of question mark (?) in the following questions?
20% of 480 + 80% of 220 + 120 – (18)2 = ?

Concepts Covered - 4

Simple pendulum

An ideal simple pendulum consists of a heavy point mass body suspended by a weightless, inextensible
and perfectly flexible string from rigid support about which it is free to oscillate.

  • The time period of oscillation of simple pendulum (T)-

When the bob is displaced to position B, through a small angle from the vertical as shown in the below figure.

   

Then Bob will perform SHM and its time period is given as

T=2πlg

where
m= mass of the bob
I = length of the pendulum
g= acceleration due to gravity.
- key points
1. The time period of a simple pendulum is independent of the mass of the bob.
I.e If the solid bob is replaced by a hollow sphere of the same radius but different mass, the time period remains unchanged.
2. Tl
where I is the distance between the point of suspension and the center of mass of the bob and is called effective length.
3. The period of a simple pendulum is independent of amplitude as long as its motion is simple harmonic.

 

           

Oscillation of Pendulum in different situations-part 1

Pendulum in a lift

1. The time period of a simple pendulum, If the lift is at rest or moving downward /upward with constant velocity.

T=2πlg

where
l= the length of the pendulum
g= acceleration due to gravity.
2. The time period of a simple pendulum, If the lift is moving upward with constant acceleration a

T=2πlg+a

where
l= the length of pendulum
g= acceleration due to gravity.
a= acceleration of pendulum.
3. The time period of a simple pendulum If the lift is moving downward with constant acceleration a

T=2πlga

where

l= the length of pendulum
g= acceleration due to gravity.
a= acceleration of the pendulum.

4. The time period of a simple pendulum, If the lift is moving downward with acceleration a=g

T=2πlgg=


It means there will be no oscillation in a pendulum as here geff=0
Similarly in the case of a satellite and at the center of the earth the geff=0 so in these cases, effective acceleration becomes zero and the pendulum will stop.
5. The time period of a simple pendulum whose point of suspension moving horizontally with acceleration 'a'

For the above figure geff=(g2+a2)12

T=2πl(g2+a2)12

Where
l= the length of pendulum
g= acceleration due to gravity.
a= acceleration of pendulum.
6. The time period of simple pendulum accelerating down an incline

In this case geff =gcosθ
T=2πlgcosΘ
where
l= the length of pendulum
g= acceleration due to gravity.
Θ= angle of inclination

 

Oscillation of Pendulum in different situations-part 2

1.The time period of the pendulum in a liquid

If we immerse a simple pendulum in a liquid, the bob of the pendulum will experience a buoyant force in an upward direction in
addition to the other forces such as gravity and tension. 

If bob a simple pendulum of density σ is made to oscillate in some fluid of density ρ (where ρ<σ.
Then the buoyant force is given as FB=Vρg
As buoyant force will oppose its weight therefore Fnet=mgeff=mgFB

For the above figure let bob be displaced for a small displacement × and is at an angle θ with the verticle.
For small displacement x of the bob, restoring force

Frest =(mgVρg)sinθ=(mgVρg)xl

and acceleration =(gVρqm)xl
On comparing with a standard equation of SHM, a=ω2x, we get

ω=(gVρgm)l=gl(1ρσ)

and T=2πg(1ρσ)=gl(1ρσ)
and T=2πg(1ρσ)
2. The time period of the Second's pendulum

Second's Pendulum: It is that simple pendulum whose time period of vibrations is two seconds.

Putting T=2sec in

T=2πlg we get the Length of a second's pendulum is near1 meter on the earth's surface. 
 

Pendulum of large length but small amplitude

If the length of the pendulum is comparable to the radius of the earth

 then T=2π1g(1l+1R)

where
l= length of pendulum
g= acceleration due to gravity.
R= Radius of earth
- Various cases
A. If lR, then 1l1R so T=2πlg
B. If lR( or l) then 1l<1R so T=2πRg=2π6.4×1061084.6 minutes and it is the maximum time period which an oscillating simple pendulum can have
C. If l=R so T=2πR2g1 hour

Study it with Videos

Simple pendulum
Oscillation of Pendulum in different situations-part 1
Oscillation of Pendulum in different situations-part 2

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

Back to top