The magnitude of the torque on a particle of mass $1 \mathrm{kg}$ is $2.5 \mathrm{N} \mathrm{m}$ about the origin. If the force acting on it is $1 \mathrm{N}$, and the distance of the particle from the origin is $5 \mathrm{m}$, the angle between the force and the position vector is (in radians):

A slab is subjected to two forces ${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$ of the same magnitude $F$ as shown in the figure. Force ${\overrightarrow{F}}_2$ is in $XY$ -plane while force $F_1$ acts along the $z-$axis at the point $(2\overrightarrow{\mathrm{i}}+3\overrightarrow{\mathrm{j}})$. The moment of these forces about point $O$ will be

A particle of mass $20 \mathrm{g}$ is released with an initial velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$ along the curve from the point $A$, as shown in figure. The point $A$ is at height $h$ from point $B$. The particle slides along the frictionless surface. When the particle reaches point $B$, its angular momentum about $O$ will be

A uniform rod is hinged as shown in the figure and is released from a horizontal position. The angular velocity of the rod as it passes the vertical position is:

A thin uniform rod of length $4 l$, mass $4 \mathrm{m}$ is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing point $O \&$ perpendicular to the plane of the papers.

Two uniform rods of equal length, but different masses are rigidly joined to form an L-shaped body, which is then pivoted about $O$ as shown in the figure. If in equilibrium the body is in the shown configuration, ratio $\frac{M}{m}$ will be:

Four forces tangent to the circle of radius $R$ are acting on a wheel as shown in the figure. The resultant equivalent one force system will be