$A$ 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
Kinetic energy of the sphere is $\frac{5}{6}\, mv^2$
Kinetic energy of the sphere is $\frac{4}{5}\, mv^2$
Angular momentum of the sphere about a fixed point on ground is $\frac{8}{3}\, mvR$
Angular momentum of the sphere about a fixed point on ground is $\frac{14}{5}\, mvR$
A particle of mass $2\, kg$ is moving such that at time $t$, its position, in meter, is given by $\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j$ . The angular momentum of the particle at $t\, = 2\, s$ about the origin in $kg\, m^{-2}\, s^{-1}$ is
A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$
Why $\vec v \times \vec p = 0$ for rotating particle ?
A particle of mass $'{m}'$ is moving in time $'t'$ on a trajectory given by
$\overrightarrow{{r}}=10 \alpha {t}^{2}\, \hat{{i}}+5 \beta({t}-5)\, \hat{{j}}$
Where $\alpha$ and $\beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for ${t}=0$ at time ${t}=$ .....$seconds.$
A fan of moment of inertia $0.6\,kg \times m^2$ is turned upto a working speed of $0.5$ revolutions per second. The angular momentum of the fan is