A stone is thrown from point $O$ on ground with velocity $\overrightarrow{v}=5\hat{\mathrm{i}}+10\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$, where $x$ is horizontal and $y$ is vertical. Its angular velocity about $O$ when the stone is at maximum height of its trajectory is

As shown in figure, a mass $m$ is rotating freely in a horizontal circle of radius $20 \mathrm{cm}$ in a smooth fixed cone which supports a stationary mass $m$ attached to the other end of the string passing through smooth hole $O$ in cone hanging vertically. Find the angular velocity of rotation $\left(\sin 53°=\frac{4}{5}\right)$.

A bead of mass $m$ is free to slide on a fixed horizontal circular wire of radius $R$. At time $t=0$, it is given a velocity $v_0$ along the tangent to the circle. If the coefficient of kinetic function between the bead and the wire is ${\mu }_k$. Then magnitude of tangential acceleration at $t=0$ will be

A small block of mass $m$ slides on a frictionless horizontal table. It is constrained to move inside a ring of radius $l$ which is fixed to the table. At $t=0$, the block has a tangential velocity $v_0$. The coefficient of friction between the block and the ring is $\mu$. The velocity of the block at time $t$ is

 A uniform rod of length $2 \mathrm{m}$. Velocity of point $B$ is $10 \mathrm{m} {\mathrm{s}}^{-1}$ as shown in figure and angular velocity of rod is  $7 \mathrm{rad} {\mathrm{s}}^{-1}$. Then

The figure shows the velocity and acceleration of a point like body at the initial moment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is