# Machine Kinematics Questions and Answers – Compound Pendulum

This set of Machine Kinematics Multiple Choice Questions & Answers (MCQs) focuses on “Compound Pendulum”.

1. Which of the following shape of the body can be considered as compound pendulum?
a) Cylindrical
b) Cubical
c) Cuboidal
d) Any rigid body

Explanation: Any rigid body having mass when suspended vertically and oscillates with small amplitude under the force of gravity undergoes SHM as a compound pendulum.

2. Compound pendulum needs to be spherical in shape.
a) True
b) False

Explanation: Any rigid body when suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. The rigid body is asssumed to have a mass and hence mass moment of inertia.

3. If the mass of the object is doubled then what will be the effect of time period of the compound pendulum?
a) Doubled
b) Remains same
c) Halved
d) Decreases by √2 times

Explanation: The time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$, now the dependency of the time period on the mass is inversely proportional to the root of mass, hence it decreases by √2 times.

4. If the mass moment inertia of the object is increased to 4 times then what will be the effect of time period of the compound pendulum?
a) Doubled
b) Remains same
c) Halved
d) Decreases by √2 times

Explanation: The time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$, now the dependency of the time period on the mass moment of inertia is directly proportional to the root of Moment of Inertia, hence it increases by 2 times.

5. Calculate the time period of an object having mass moment of inertia = 100 Kg-m2, mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.
a) 14.1
b) 15.2
c) 13.3
d) 12.9

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$
substituting the values we get
T = 14.1 sec.

6. Calculate the frequency of vibration in Hz of an object having mass moment of inertia = 100 Kg-m2, mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.
a) 0.14
b) 0.15
c) 0.13
d) 0.07

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$
substituting the values we get
T = 14.1 sec.
f = 1/T = 0.07 Hz.

7. Calculate the moment of inertia of an object having time period = 14 sec, mass of 10 Kg and the centre of gravity lies at a point 20 cm below the point of suspension.
a) 94.1
b) 95.2
c) 93.3
d) 97.4

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$
substituting the values we get
I = 97.4 Kg-m2.

8. All simple pendulums are compound pendulums.
a) True
b) False

Explanation: Simple pendulum also is a compound pendulum where the mass is a point mass, hence the distance from centre of gravity is the length of the string.

9. If the mass moment inertia of the object is increased to 4 times then what will be the effect of time period of the simple pendulum?
a) Doubled
b) Remains same
c) Halved
d) Decreases by √2 times

Explanation: The time period of a simple pendulum is given by:
(2π)√(I/g), now the dependency of the time period on the mass moment of inertia is non existent, hence it remains unchanged.

10. Calculate the moment of inertia of an object having time period = 14 sec, mass moment of inertia= 100 Kg-m2 and the centre of gravity lies at a point 20 cm below the point of suspension.
a) 9.1
b) 9.2
c) 9.3
d) 10.2

Explanation: From the given data it is clear that the given rigid body constitutes a compound pendulum, now the time period of a compound pendulum is given by:
(2π)$$\sqrt{(\frac{I}{mgl})}$$
substituting the values we get
m = 10.2 Kg.

Sanfoundry Global Education & Learning Series – Machine Kinematics.

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