A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega $. Its centre of mass will rise upto maximum height

- A
$\frac{1}{6}\frac{{l\,\omega }}{g}$

- B
$\frac{1}{2}\frac{{{l^2}{\omega ^2}}}{g}$

- C
$\frac{1}{6}\frac{{{l^2}{\omega ^2}}}{g}$

- D
$\frac{1}{3}\frac{{{l^2}{\omega ^2}}}{g}$

In the given figure linear acceleration of solid cylinder of mass $m_2$ is $a_2$. Then angular acceleration $\alpha_2$ is (given that there is no slipping).

Three masses of $2\,kg$, $4\, kg$ and $4\, kg$ are placed at the three points $(1, 0, 0)$ $(1, 1, 0)$ and $(0, 1, 0)$ respectively. The position vector of its center of mass is

What is the torque of force $\vec F = 2\hat i - 3\hat j + 4\hat k$ acting at a point $\vec r = 3\hat i + 2\hat j + 3\hat k$ about the origin?

$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.

If the equation for the displacement of a particle moving on a circular path is given by:

$\theta = 2t^3 + 0.5$

Where $\theta $ is in radian and $t$ in second, then the angular velocity of the particle at $t = 2\,sec$ is $t=$ ....... $rad/sec$