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**Hint:**Assume the position vectors and velocity vectors of the centre of the disc and any other point a on the disc. Find the relation between the position vectors of two points and the velocity vectors. Then, consider the motion about the instantaneous axis and verify the options.

**Complete answer:**

Let c be the centre of the disc with position vector ${{\vec{r}}_{c}}$ and velocity vector ${{\vec{v}}_{c}}$. Let a be a general point on the disc having position vector ${{\vec{r}}_{a}}$. Let $\vec{\omega }$be the angular velocity of the system as given in the problem and $\vec{\omega }'$ be the angular velocity about the instantaneous axis. The velocity of point c and point a are given by ${{\vec{v}}_{a}}=\vec{\omega }\times {{\vec{r}}_{a}}$ hand ${{\vec{v}}_{c}}=\vec{\omega }'\times {{r}_{c}}$. Also, considering the motion about the instantaneous axis,

${{\vec{v}}_{a}}={{\vec{v}}_{c}}+\vec{\omega }'\times ({{\vec{r}}_{a}}-{{\vec{r}}_{c}})$

Substitute ${{\vec{v}}_{a}}$value in the above equation, we get

$(\vec{\omega }'-\vec{\omega })\times ({{r}_{a}}-{{r}_{c}})=0$

Now, as the radius vector is any general vector on the disc, the above equation is satisfied only when $\vec{\omega }'=\vec{\omega }$. This argument will be true for both cases. Therefore, the instantaneous axis for both the cases are parallel to the z axis and angular speed about these aces are equal.

**Correct option is option a.**

**Additional information:**

Rigid body is an idealization of a solid body where the deformations occurring on the body are neglected. In other words, the distance between any 2 given points of rigid body remains constant regardless of the external force acting upon it. The concept of rigid body and rigid body dynamics was developed to solve a range of problems that could not be explained with classical physics. Best examples to demonstrate this is the motion of rotation of the fan, a potter’s wheel, etc. Which we cannot explain by assuming mass. In real life in the case of a body such as wheels and steel rods, bending is negligible, so we treat those bodies as a rigid body.

**Note:**

A system which can have translational and rotational motion, when rotated with an angular speed, the motion at any instant can be taken as a combination of rotation of the centre of mass of the disc about any axis, rotation of the disc through an instantaneous vertical axis passing through centre of mass.

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