In a rectangle $ABCD (BC = 2AB)$, the moment of inertia along which axis will be minimum ?
$BC$
$BD$
$HF$
$EG$
If the equation for the displacement of a particle moving on a circular path is given by:
$\theta = 2t^3 + 0.5$
Where $\theta $ is in radian and $t$ in second, then the angular velocity of the particle at $t = 2\,sec$ is $t=$ ....... $rad/sec$
If the earth were to suddenly contract to $\frac {1}{n}^{th}$ of its present radius without any change in its mass the duration of the new day will be nearly
A long horizontal rod has a bead which can slide along its length, and initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is $\mu$, and gravity is neglected, then the time after which the bead starts slipping is
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
$A$ non uniform rod $OA$ of linear mass density $\lambda = \lambda_0x$ $(\lambda_0 =$ const.) is suspended from ceiling with hinge joint $O$ & light string as shown in figure. Find the angular acceleration of rod just after the string is cut.