A particle is moving in a circular path of radius $a,$ with a constant velocity $v$ as shown in the figure.The centre of circle is marked by $'C'$. The angular momentum from the origin $O$ can be written as
$va\,\, ( 1 + cos\,2\theta )$
$va\,\, ( 1 + cos\,\theta )$
$va\,\,cos\,2\theta $
$va$
$A$ hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$. It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$. If it purely rolls
$A$ block of mass $m$ moves on a horizontal rough surface with initial velocity $v$. The height of the centre of mass of the block is $h$ from the surface. Consider a point $A$ on the surface.
$A$ particle of mass $2\, kg$ located at the position $(\hat i + \hat j)$ $m$ has a velocity $2( + \hat i - \hat j + \hat k)m/s$. Its angular momentum about $z$ -axis in $kg-m^2/s$ is
A particle of mass $m$ is projected with a velocity $v$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is
$A$ ball of mass $m$ moving with velocity $v$, collide with the wall elastically as shown in the figure.After impact the change in angular momentum about $P$ is: