A particle of mass $= 5\ units$ is moving with a uniform speed $V = 3 \sqrt 2\ units$ in the $XOY$ Plane along the line $Y = X+4 $ . The magnitude of the angular momentum of the particle about the origin is ...... $unit.$
$60$
$40 \sqrt 2$
$0$
$7.5$
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
Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when speed of $A$ is $v$ and speed of $B$ is $2v$, speed of center of mass of the system is
In the given figure linear acceleration of solid cylinder of mass $m_2$ is $a_2$. Then angular acceleration $\alpha_2$ is (given that there is no slipping).
A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of free end of the stick if the string is cut? (in $rad/sec^2$ )
Particles of masses $m, 2m, 3m, ...... nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,...., nl\, cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point (in centimetres) is