Topic 4: Simple Pendulum

Simple Pendulum

A simple pendulum consists of a small heavy bob suspended from a rigid support by a light, inextensible string.

When the bob is displaced slightly from its mean position and released, it oscillates to and fro.

Conditions for Simple Pendulum to Perform SHM

The oscillations should be small
The string should be light and inextensible
The bob should be considered as a point mass

Time Period of Simple Pendulum

For small oscillations, the motion of a simple pendulum is simple harmonic.

The time period of a simple pendulum is given by:

T = 2π √(L / g)

where,
L = length of the pendulum (m)
g = acceleration due to gravity (m s⁻²)

Important Observations

Time period is independent of mass of the bob
Time period is independent of amplitude (for small angles)
Time period depends on length and value of g

Effect of Length and Gravity

Increase in length → time period increases
Increase in g → time period decreases

Q1. A simple pendulum consists of:
A) Heavy string and light bob
B) Light string and heavy bob
C) Elastic string and bob
D) Rigid rod and bob

Answer: B


Q2. Time period of a simple pendulum depends on:
A) Mass of bob
B) Amplitude
C) Length of pendulum
D) Shape of bob

Answer: C


Q3. Formula for time period of a simple pendulum is:
A) T = 2π √(g / L)
B) T = π √(L / g)
C) T = 2π √(L / g)
D) T = √(L / g)

Answer: C


Q4. Time period of a simple pendulum is independent of:
A) Length
B) Gravity
C) Mass of bob
D) Value of π

Answer: C


Q5. If length of a pendulum is doubled, its time period becomes:
A) Double
B) Half
C) √2 times
D) 2√2 times

Answer: C


Q6. If g increases, the time period of pendulum:
A) Increases
B) Decreases
C) Remains same
D) Becomes zero

Answer: B


Q7. Simple pendulum performs SHM when oscillations are:
A) Large
B) Very large
C) Small
D) Random

Answer: C


Q8. Unit of length in pendulum formula is:
A) cm
B) mm
C) meter
D) km

Answer: C

Chapter 10: Oscillations

Topic 4: Simple Pendulum – Quick Revision

1. Simple Pendulum

A heavy bob suspended by a light, inextensible string.

2. Time Period

T = 2π √(L / g)

3. Depends On

Length of pendulum
Acceleration due to gravity

4. Independent Of

Mass of bob
Amplitude (for small oscillations)

Exam Focus (MHT-CET)

Numericals are frequently asked on change in time period due to change in length or gravity.

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