If the angular velocity of a merry-go-round is $60^o/sec$ and you are $3.5\,m$ from the centre of rotation, your linear velocity will be

The angular momentum of a projectile projected at an angle $\theta $ with the horizontal with speed $u$ about the point of projection when it is at the highest point of its trajectory is

$A$ particle of mass $m$ is projected with a velocity $u$ making an angle $45^o$ with the horizontal. The magnitude of the torque due to weight of the projectile, when the particle is at its maximum height, about the point of projectile

If the density of material of a circular plate and a square plate as shown is same, the centre of mass of the composite system will be 

A thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........

The torque of the force $\overrightarrow F = (2\hat i - 3\hat j + 4\hat k\,)N$ acting at the point $\overrightarrow {r\,} = (3\hat i + 2\hat j + 3\hat k)\,m$ about the origin be