A non uniform cylinder of mass $m$ , length $l$ and radius $r$ is having its cetnre of mass at a distance $l/4$ from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density $\rho $ . The moment of inertia of the rod about the centre of mass is $I$ . The angular acceleration of point $A$ relative to point $B$ just after the rod is released from the position shown in figure is
$\frac{{\pi \rho g{l^2}{r^2}}}{I}$
$\frac{{\pi \rho g{l^2}{r^2}}}{4I}$
$\frac{{\pi \rho g{l^2}{r^2}}}{2I}$
$\frac{{3\pi \rho g{l^2}{r^2}}}{4I}$
$A$ right triangular plate $ABC$ of mass $m$ is free to rotate in the vertical plane about a fixed horizontal axis through $A$. It is supported by a string such that the side $AB$ is horizontal. The reaction at the support $A$ is:
A uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. A string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is
A uniform rod $AB$ is suspended from a point $X$, at a variable distance from $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m, x)$ values is recorded. The appropriate variable that give a straight line, when plotted, are
A uniform metal plate shaped like a triangle $A B C$ has a mass of $540 \,g$. The length of the sides $A B, B C$ and $C A$ are $3 \,cm , 5 \,cm$ and $4 \,cm$, respectively. The plate is pivoted freely about the point $A$. What mass must be added to a vertex, so that the plate can hang with the long edge horizontal?
A uniform rod of mass $15\,kg$ and length $5\,m$ is held stationary with the help of a light string as shown. Then tension in the string is ......... $N.$