$A$ wheel is rolling straight on ground without slipping. If the axis of the wheel has speed $v$,the instantaneous velocity of a point $P$ on the rim,defined by angle $\theta$ relative to the vertical,relative to the ground will be:

Consider a point $P$ on the circumference of a disc of radius $R$ rolling along a horizontal surface. The distance traveled by point $P$ in one full rotation of the disc is:

$A$ uniform solid cylinder of mass $m$ and radius $R$ is set in rotation about its axis with an angular velocity $\omega_0$,then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and plane is equal to $\mu$. The time after which the cylinder starts rolling without slipping is

$A$ wheel of radius $2 \ cm$ is at rest on a horizontal surface. $A$ point $P$ on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface,the displacement of point $P$ after half a rotation of the wheel is:

$A$ boy is pushing a ring of mass $2 \ kg$ and radius $0.5 \ m$ with a stick as shown in the figure. The stick applies a force of $2 \ N$ on the ring and rolls it without slipping with an acceleration of $0.3 \ m/s^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs,and the coefficient of friction between the stick and the ring is $(P/10)$. The value of $P$ is

$A$ wheel of radius $r$ is rolling on a straight line,with the velocity of its centre being $v$. At a certain instant,the point of contact of the wheel with the ground is $M$ and $N$ is the highest point on the wheel (diametrically opposite to $M$). Which of the following statements is incorrect?