System of Parti...

A disc of radius r rolls on without slipping on a rough horizontal floor. If velocity of its centre of mass is v then velocity of point p, as shown in the figure $$\left[ O P = \left( \cfrac { r } { 2 } \right) \text { and } \angle Q O P = 60 ^ { \circ } \right]$$  is-

Locate centre of mass of a uniform semicircular loop of radius R (shown in figure)

The maximum tension that an inextensible ring of radius  1m and mass density 0.1 $$kg\;{m^{ - 1}}$$ can bear is 40 N. The maximum angular velocity with which it can be rotated in a  circular path is.

A uniform disc of mass m and radius R is rotating with angular velocity $$ \omega $$ on a smooth horizontal surface. another identical disc is moving translationally with velocity v as shown.
when they touch each other, they stick together. the angular velocity of centre of mass of the system after contact will be 

A particle  $$P$$  strikes the rod  $$R$$  perpendicularly as shown. The rod is suspended vertically with upper end hinged $$\left( x = \dfrac { 1 } { 2 } , \text { elastic collision } \right)$$  Then select correct statement:

A uniform thick plate in the shape of an arrow head has dimensions as shown in the given figure. The centre of mass lies at a point.

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the centre of the disc, the distance $$x_2$$ of the centre of mass of the remaining part from the initial centre of mass O is given by:-

Two rods of equal mass m and length $$l$$ lie along the $$  x  $$ axis and $$  y  $$ axis with their centres at the origin.What is the moment of inertia of both about the line $$  x=y : $$

Select correct statement  regarding centrn of mass 

A uniform metre rule of mass 100$$\mathrm { g }$$ is balanced on afulcrum at mark 40$$\mathrm { cm }$$ by suspending an unknownmass $$m$$ at the mark 20$$\mathrm { cm } .$$