A $T-$ shaped object of uniform thickness and same material with dimensions shown in the figure, is lying on a smooth floor. A force $\vec F$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$
$\frac {4l}{3}$
$l$
$\frac {2l}{3}$
$\frac {3l}{2}$
The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta (t) = 2t^3 -6t^2$. The torque on the wheel becomes zero at $t$ $=$ ........ $\sec.$
If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass, the duration (in $hrs.$ ) of the new day will be nearly
$ ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moment of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct
$A$ bob of mass $m$ is attached to a string whose other end is tied to a light vertical rod as shown in figure. The bob is swinging in horizontal plane with constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is minimum friction coefficient between ground and block for which block does not slip ?
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be