﻿ A disc and a sphere of the same radius but differnt masses roll off two inclined planes of the same altitude and length. which one of the two objects gets to the bottom of the plane first? from Physics System of Particles and Rotational Motion Class 11 Manipur Board

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A disc and a sphere of the same radius but differnt masses roll off two inclined planes of the same altitude and length. which one of the two objects gets to the bottom of the plane first?

• Sphere

• Both reach at the same time

• Depends on their masses

• Disc

A.

Sphere

a) Acceleration of an object rolling down an inclined plane is given by,

m = mass of the object,
I = moment of Inertia about the axis through the centre of mass.

For solid sphere,

For hollow sphere,

Therefore, the given sphere is a solid sphere.

asolid sphere = ahollow sphere > adisk

a) Acceleration of an object rolling down an inclined plane is given by,

m = mass of the object,
I = moment of Inertia about the axis through the centre of mass.

For solid sphere,

For hollow sphere,

Therefore, the given sphere is a solid sphere.

asolid sphere = ahollow sphere > adisk

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Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated.
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What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system.
794 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object.
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Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion.
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Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
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