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
$\sqrt{10 g h / 7}$
$\sqrt{7 g h / 5}$
$\sqrt{5 g h / 7}$
$\sqrt{2 g h}$
Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is ...... $J$
A disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/\sec .$ Its rotational kinetic energy is
A body is rolling down an inclined plane. If kinetic energy of rotation is $40\%$ of translational kinetic energy, then the body is a
If $L, M$ and $P$ are the angular momentum, mass and linear momentum of a particle respectively which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius $R$
An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg - m ^2$