A rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in figure. When string is cut, the initial angular acceleration of the rod is
$\frac{{2g}}{{3L}}$
$\frac{{3g}}{{2L}}$
$g/L$
$2g/L$
A particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$ . If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$ , then
A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega $ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is
An object slides down a smooth incline and reaches the bottom with velocity $v$. If same mass is in the form of a ring and it rolls down an inclined plane of same height and angle of inclination, then its velocity at the bottom of inclined plane will be ............
When helical gear $M$ turns as shown, gears $I$ & $H$ turn in the following manner. Which of the following is correct ? (Assuming no slipping anywhere)
Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat i +\hat j+ \hat k$ and $-\hat i -\hat j -\hat k$ respectively would have the centre of mass at