A hole of radius $\frac{R}{2}$ is cut from a thin circular plate of radius $R$ and mass $M.$ The moment of inertia of the plate about an axis through $O$ perpendicular to the $x-y$ plane (i.e. about the $z-$axis) is

A spool is pulled horizontally by two equal and opposite forces as shown in the figure. Which of the following statements is correct?

A ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0.$ The kinetic energy of the system in case of no slipping is

These questions consist of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: Moment of inertia about an axis passing through the centre of mass is always minimum.

Reason: Theorem of parallel axis can be applied for $2-\mathrm{D}$ as well as $3-\mathrm{D}$ bodies.

These questions consist of two statements each printed as assertion and reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: A sphere is placed in pure rolling condition over a rough inclined surface. Then, force of friction will act in downward direction.

Reason: Angular acceleration (actually retardation) due to friction is anti-clockwise.

These questions consists of two statements each printed as assertion and reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: A ring and a disc of same mass and radius begin to roll without slipping from the top of an inclined surface at $t=0.$ The ring reaches the bottom of incline in time $t_1$ while the disc reaches the bottom in time $t_2,$ then $t_1<t_2$
Reason: Disc will roll down the plane with more acceleration, because of its lesser value of moment of inertia.

These questions consists of two statements each printed as assertion and reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: A body is moving along a circle with a constant speed. Its angular momentum about the centre of the circle remains constant.

Reason: In this situation, a constant non-zero torque acts on the body.