MHT-CET Physics Crash Course “Conical Pendulum” Class 12

“Conical Pendulum” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics

In this session G.S. Khairnar will discuss the theory and MCQ’s of “Conical Pendulum”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

Conical Pendulum:-

Hello everyone, we know that in circular motion centripetal force, centrifugal force is present so as to complete circular path by object. In certain cases these forces have different formats but similar meaning, e.g. if a stone is tied to a thread and whirled in circular motion, tension acting on the string is nothing but the centripetal force required for circular motion.

Conical pendulum also uses the same format for centripetal force.

Let’s discuss the concept of conical pendulum in detail……!

Conical Pendulum:

A small heavy point mass suspended by a light and inextensible string from a rigid support and revolving in a horizontal circle with a uniform speed constitutes a conical pendulum.

Consider a bob of pendulum of mass ‘m’ tied to the string of length ‘l’ and suspended from rigid support as shown in fig.

When bob revolved in a horizontal circle, the traces out a cone. Let ‘r’ be the radius.

1) The vertical component Tcosθ which is balanced by weight mg

∴ Tcosθ = mg ………………….(1)

2) The horizontal component Tsinθ which is directed towards center of the circle and it provides the necessary centripetal force.

Period of conical pendulum (T₁):

The Period of conical pendulum is given by,

Period of conical pendulum depends upon:-

• Length of pendulum.
• Angle of inclination to vertical.
• Acceleration due to gravity.

And it is independent of mass of bob.

Conical Pendulum:

Let’s solve the following MCQ’s on conical pendulum:

Q.1) The component of tension that balances the weight of conical pendulum is….

a) Tcosθ

b) Tsinθ

c) Tcotθ

d) Ttanθ

Answer

a) Tcosθ

Q.2) Centripetal force required for circular motion of bob of conical pendulum is provided by ….

a) Tcosθ

b) Tsinθ

c) Tcotθ

d) Ttanθ

Answer

b) Tsinθ

Q.3) Linear velocity of bob of conical pendulum performing horizontal circular motion is……..

Q.4) Angular velocity of conical pendulum is……..

a) directly proportional to height of pendulum

b) directly proportional to square root height of pendulum

c) inversely proportional to square of height of pendulum

d) inversely proportional to square root height of pendulum

Answer

d) inversely proportional to square root height of pendulum

Q.5) Angular velocity of conical pendulum performing circular motion of radius 10 cm and length 40 cm is……..

a) 8.10 rad/s

b) 8.10 m/s

c) 8.10 cm/s

d) 8.10 rpm

Answer

a) 8.10 rad/s

Q.6) Period of conical pendulum is given as….

Q.7) Ratio of periods of conical pendulums is 2:3, and the ratio of angle made by strings with the vertical is √3:1, the ratio of lengths of pendulum is ……………..

Q.8) What will be period of conical pendulum on the planet where acceleration due to gravity is 1/9^th of value of earth.……………..

a) T

b) 3 T

c) 1/9

d) 9 T

Answer

b) 3 T

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