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The moment of inertia of a particle of mass m kept at point (a, b) on the x-y plane about the x-axis is
- a)mab
- b)ma2
- c)mb2
- d)m(a2 + b2)1/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The moment of inertia of a particle of mass m kept at point (a, b) on ...
Moment of inertia:
- Moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
- The moment of inertia of a particle is
⇒ I = mr2
Where r = the perpendicular distance of the particle from the rotational axis.
- Moment of inertia of a body made up of a number of particles (discrete distribution)
⇒ I = m1r12 + m2r22 + m3r32 + m4r42 + -------
EXPLANATION:
Given: mass of the particle = m, distance from x-axis = b.
The moment of inertia for the particle of mass m from an axis at a distance b is,
⇒ I = mb2
Therefore option 3 is correct.
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The moment of inertia of a particle of mass m kept at point (a, b) on ...
Explanation:
The moment of inertia of a particle about an axis is given by the product of the mass of the particle and the square of its perpendicular distance from the axis. In this case, we need to find the moment of inertia of a particle of mass m kept at point (a, b) on the x-y plane about the x-axis.
Steps to find the moment of inertia:
- The perpendicular distance of the particle from the x-axis is b.
- The moment of inertia of the particle about the x-axis is given by the formula I = m * b^2.
- Substituting the value of b, we get I = m * (b)^2 = mb^2.
Therefore, the moment of inertia of a particle of mass m kept at point (a, b) on the x-y plane about the x-axis is mb^2. Hence, option 'c' is the correct answer.
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