The axis of rotation is the line on which the centers of circles lie and it is perpendicular to the plane of circles. Calculate the moment of inertia of a 1 kg point mass placed at a point P (2 m, 4 m), taking x-axis as the axis of rotation.

- When a body rotates, all the particles of the body perform circular motion.
- The axis of rotation is the line on which the centers of circles lie and it is perpendicular to the plane of circles.

- Consider a small particle 'A' of a rotating body.

- To find the perpendicular distance of 'A' from the axis of rotation, visualize the figure showing the path of particle A such that the axis is seen as a point 'P' i.e., the line of sight is the axis of rotation.

- Then, the distance between 'A' and 'P' would be the perpendicular distance of particle 'A' from the axis of rotation.

A rA= a/2, rB= a/2, rC= a/2, rD= a/2

B rA= a, rB= a, rC= a, rD= a

C rA= 2a, rB= 2a, rC= 2a, rD= 2a

D None of these

- Moment of inertia of discrete particles of varying masses of a body about the given axis is defined as \(I=\sum m_i\;r_i^2\)

where, \(m_i\) is the mass of the i^{th} particle and \(r_i\) is the perpendicular distance of the i^{th }particle from the axis of rotation.

A \(\dfrac {m\ell^2}{2}\)

B \(\dfrac {m\ell^2}{4}\)

C \(\dfrac {2m\ell^2}{5}\)

D \(\dfrac {2m\ell^2}{3}\)

- Moment of inertia of discrete particles of varying masses of a body about the given axis is defined as \(I=\sum m_i\;r_i^2\)

where, \(m_i\) is the mass of the i^{th} particle and \(r_i\) is the perpendicular distance of the i^{th }particle from the axis of rotation.

A \(m\dfrac {a^2}{3}\)

B \(m\dfrac {a^2}{2}\)

C \(ma^2\)

D \(\dfrac {2ma^2}{3}\)

- Moment of inertia of a point mass M, which is at a perpendicular distance R from the axis of rotation is defined as :

\(I=MR^2\)

**Note :** R does not depend upon the point of application of force.

A 8 kg m2

B 16 kg m2

C 5 kg m2

D 2 kg m2

- Moment of inertia of discrete particles of varying masses of a body about the given axis is defined as \(I=\sum m_i\;r_i^2\)

where, \(m_i\) is the mass of the i^{th} particle and \(r_i\) is the perpendicular distance of the i^{th }particle from the axis of rotation.

A \(8m\ell^2\)

B \(5m\ell^2\)

C \(9m\ell^2\)

D \(3m\ell^2\)

^{th} particle and \(r_i\) is the perpendicular distance of the i^{th }particle from the axis of rotation.

A \(ma^2\)

B \(2ma^2\)

C \(3ma^2\)

D \(4ma^2\)