“Simple Pendulum and its Laws” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Simple Pendulum and its Laws”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Simple Pendulum and its Laws:-
Hello dear students we have learnt about an oscillatory motion in detail. An oscillatory motion is periodic motion. The ‘to’ and ‘fro’ motion of object along the fixed path is nothing but oscillations. We also know about the linear simple harmonic motion, in which the particle performing oscillatory motion and restoring force always acts towards the mean position.
Oscillatory Motion:-
The motion of body is along the same path i.e. towards left of mean position and then towards right (to and fro). Such type of motion is called as oscillatory motion. One complete set of such motion is called as an ‘Oscillation’. The basic form of oscillatory motion is nothing but simple harmonic motion.
E.g-i) The motion of pendulum in a clock.
In this article we are going to study the motion of simple pendulum and obtain an expression for period of simple pendulum.
Ideal Simple pendulum:–
A heavy point mass suspended from rigid support by a massless, inextensible and twist less string is called Ideal simple pendulum.
In practice, ideal simple do not exist because no string can be perfectly massless and inextensible.
Let’s define and learn the concept of simple pendulum in detail……..!
Definition:
Laboratory Simple pendulum:–
A heavy point mass suspended from rigid support by a light weight and slightly extensible string is called Laboratory simple pendulum.
Consider the heavy point mass ‘m’ suspended from rigid support using a string of length ‘l’. Let the pendulum is displaced through angle θ from its mean position and oscillates with amplitude ‘x’. As shown in fig below.
When pendulum is at displaced position its weight is resolved into two components as below,
mgcosθ – balances the tension in the string.
mgsinθ –provides restoring force, due to which pendulum is oscillating about its mean position.
Negative sign indicates that acceleration and displacement are oppositely directed.
From equation (3) it is clear that the acceleration is directly proportional to the displacement. Hence simple pendulum performs linear SHM.
Period of Simple Pendulum: – Time taken by the simple pendulum to complete one oscillation is called as period of simple pendulum.
We know that the period of simple pendulum is given as,
Using above equation we can find the period of simple pendulum.
Some important law related to simple pendulum………!
- Law of mass – Period of simple pendulum is independent of mass of pendulum.
- Law of length – Period of simple pendulum is directly proportional to square root of length of pendulum.
- Law of acceleration due to gravity– Period simple pendulum is inversely Proportional Square to acceleration due to gravity.
- Law of isochronous – Period of simple pendulum is independent of amplitude of oscillation.
- Second’s Pendulum:-
A pendulum whose time period is 2 seconds is called second’s pendulum.
The time period of simple pendulum is given by,
i.e. when the length of simple pendulum is approximately of 100 cm or 1 m, the pendulum is said to second’s pendulum.
Simple Pendulum and its Laws:-
Let’s solve the MCQ’s based on simple pendulum…!
Q.1) The period of simple pendulum is independent of……
a) Length of pendulum
b) mass of bob
c) acceleration due to gravity
d) all of these
Answer
b) mass of bob
Q.2) The period of simple pendulum is ……
a) directly proportional to length of pendulum
b) directly proportional to square of length of pendulum
c) directly proportional to square root of length of pendulum
d) none of these
Answer
c) directly proportional to square root of length of pendulum
Q.3) If the acceleration due to gravity at the point is nine times the present value, the period of simple pendulum will be ……
Q.4) Simple pendulum was oscillating with amplitude of 4 cm for 2 min. Now the amplitude of oscillation is increased to cm for next 2 min. The period of simple pendulum will be ……
a) increased by 4
b) decreased by 4
c) initially decreased and then increased by 4
d) remains same
Answer
d) remains same
Period of simple pendulum is independent of amplitude of oscillation.
Q.5) The ratio of period of two pendulums is 2:3 oscillating at two different planets having the acceleration due to gravity in ratio 1:9. The ratio of lengths of the pendulum will be……
Q.6) The length of second’s pendulum on the planet where the acceleration due to gravity is half that of earth is……
a) twice that of earth
b) half that of earth
c) same as that of earth
d) can not predicted
Answer
b) half that of earth
For second^’ pendulum we have,
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