A rigid body in shape of a triangle has $v_A=5 \mathrm{m}/\mathrm{s}$ $\downarrow$, $v_B=10 \mathrm{m}/\mathrm{s}$ $\downarrow$. Find velocity of point C.

A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

A rod of length $50 cm$ is pivoted at one end. It is raised such that it makes an angle of ${30}^o$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad s^{-1}$ ) will be $\left(g=10 m{s}^{-2}\right)$

A solid sphere rolls without slipping, first horizontally and then up to a point $x$ at height $h$ on an inclined plane before rolling down, as shown in the figure below.

The initial horizontal speed of the sphere is

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $AB$ is (g-acceleration due to gravity)

A rigid ball rolls without slipping on a surface shown below.

Which on the following is the most likely representation of the distance travelled by the ball vs time graph?

On a pulley of mass $M$ hangs a rope with two masses $m_1$ and $m_2\left(m_1>m_2\right)$ tied at the ends as shown in the figure. The pulley rotates without any friction, whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?