System of Parti...

An insect of mass m is initially at rest at the one end of a stick length L and mass M, which rests on a smooth horizontal floor. The coefficient of friction between the insect and stick is k. The insect starts moving to reach the other end in shortest possible time. Choose the incorrect statement.

The angular speed of a body changes from $$ \omega_1 $$ to $$ \omega_2 $$ without applying a torque but due to change in its moment of inertia.the ratio of radii of gyration in the two cases is

A woman of mass m stands at the edge of a solid cylindrical platform of mass $$M$$ and radius $$R$$. At $$t=0$$ the platform is rotating with negligible friction at angular velocity $${ \omega  }_{ 0 }$$ about a vertical axis passing through the centre. The woman begins to walk with speed v, relative to the platform, towards the center of the platform.

A body of mass $$m$$ moves in a circular path with uniform angular velocity. The motion of the body has constant

A simple pendulum of mass $$m$$ executes $$SHM$$ with total energy $$E$$. If at an instant it is at one of extreme positions, then its linear momentum after a phase shift of $$\dfrac { \pi  }{ 3 }\ rad$$ will be

Four masses are joined to a light circular frames in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be (where a is the radius of the circle)

A child is standing at one end of long trolley moving with a speed V on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u the centre of mass of the system(trolley +child) will move with a speed 

For a particle showing motion under the force $$F=-5{ \left( x-2 \right) },$$ the motion is

$$1 J$$ of work is required to stop an iron rim from rolling on a horizontal floor.The mass and the radius of the rim are $$3 \text { kg and } 40 \mathrm { cm }$$ respectively. What is the speed of the centre of mass of the rim?

In the figure shown $$ABC$$ is a uniform wire. If centre of mass of wire lies vertically below point $$A$$, then $$\cfrac{BC}{AB}$$ is close to: