Which one of the following four graphs best depicts the variation with $x$ of the moment of inertia $I$ of a uniform triangular lamina about an axis parallel to its base at a distance $x$ from it?

$A$ circular hoop of mass $m$ and radius $R$ rests flat on a horizontal frictionless surface. $A$ bullet,also of mass $m$ and moving with a velocity $v$,strikes the hoop and gets embedded in it. The thickness of the hoop is much smaller than $R$. The angular velocity with which the system rotates after the bullet strikes the hoop is

$A$ cubical block of side $a = 30\,cm$ is moving with velocity $v = 2\,m/s$ on a smooth horizontal surface. The surface has a small bump at a point $O$ as shown in the figure. The angular velocity (in $rad/s$) of the block immediately after it hits the bump is:

$A$ uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a vertical plane. The rod is released from a horizontal position. When the rod becomes vertical,the reaction force at the pivot is:

$A$ metal rod of length $L$ and mass $m$ is pivoted at one end. $A$ thin disk of mass $M$ and radius $R$ $(R < L)$ is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case $A$) The disc is not free to rotate about its center and (case $B$) the disc is free to rotate about its center. The rod-disc system performs $SHM$ in a vertical plane after being released from the same displaced position. Which of the following statement$(s)$ is (are) true?

$A$ disc of circumference $s$ is at rest at a point $A$ on a horizontal surface when a constant horizontal force begins to act on its centre. Between $A$ and $B$ there is sufficient friction to prevent slipping,and the surface is smooth to the right of $B$. $AB = s$. The disc moves from $A$ to $B$ in time $T$. To the right of $B$,