$A$ uniform sphere of radius $R$ and mass $m$ is placed on an inclined plane which makes an angle $45^{\circ}$ to the horizontal. For which of the following values of the coefficient of friction does the sphere roll without slipping? Select the incorrect option.

$A$ solid sphere rolls down from the top of an inclined plane,$7 \ m$ high,without slipping. Its linear speed at the foot of the plane is $\left(g = 10 \ m/s^2\right)$

$A$ rolling wheel of $12 \, kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \, kg$ through a string of fixed length and a pulley as shown in the figure. Consider $PR$ as a friction-free surface. The velocity of the centre of mass of the wheel when it reaches the bottom $Q$ of the inclined plane $PQ$ will be $\frac{1}{2} \sqrt{xgh} \, m/s$. The value of $x$ is.............

$A$ ball rolls down an inclined plane,as shown in the figure. The ball is first released from rest from $P$ and then later from $Q$. Which of the following statement$(s)$ is/are correct?
$(i)$ The ball takes twice as much time to roll from $Q$ to $O$ as it does to roll from $P$ to $O$.
$(ii)$ The acceleration of the ball at $Q$ is twice as large as the acceleration at $P$.
$(iii)$ The ball has twice as much $K.E.$ at $O$ when rolling from $Q$ as it does when rolling from $P$.

$A$ solid cylinder and a solid sphere of same mass and radius roll without slipping on a rough inclined plane. The force of friction is ..........

$A$ solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \ m/s$ at the bottom of the inclination. How far will the ball go up the plane (in $cm$)? (Use $g=10 \ m/s^2$)