A plank is moving in a horizontal direction with a constant acceleration $\alpha \hat{ i }$. A uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank. Let the centre of mass of the block be at $(0, l / 2)$ at a given instant. If $\alpha =g / 10$, then the normal reaction exerted by the plank on the block at that instant acts at
$(0,0)$
$(-l / 20,0)$
$(-l / 10,0)$
$(l / 10,0)$
Three particles are connected by massless rods lying along the $y-$ axis. If the system rotates about the $x-$ axis with an angular speed of $2\, rad/s$, the $M.I.$ of the system is ......... $kg-m^2$
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 circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$
If $\vec F$ is the force acting on a particle having position vector $\vec r$ and $\vec \tau $ be the torque of this force about the origin, then
$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strike the rod with a velocity $v_0$ at point $C$ a distance $x$ from the centre $O$. The particle comes to rest after collision. The value of $x$, so that point $A$ of the rod remains stationary just after collision, is :