System of Parti...

Two objects, a ring and a spherical shell of same mass and radius are released from the top of two identical inclined plane. If they are rolling without slipping, then ratio of speed of center of mass of the two objects when they will reach the bottom of the inclined plane is

A solid sphere is thrown on a horizontal rough surface with initial velocity of centre of mass u  without rolling. Velocity of its centre of mass when it starts pure rolling is 

A satellite is revolving around a planet in a circuit orbit of radius. $$'r'$$ and has angular momentum $$L$$. If it is taken into a higher orbit of radius $$'4r'$$, the charge in its angulatr momentum is

Line $$PQ$$ is parallel to y-axis and moment of inertia of a rigid body about $$PQ$$ line is given by $${\rm I} = 2{x^2} - 12x + 27$$ where $$x$$ is in meter and $${\rm I}$$ is in $$Kg - {m^2}$$ The minimum value of $${\rm I}$$ is  :

Length width and mass of a rectangular plate are l, b and m respectively. The radius of gyration about the axis passing through centre and perpendicular to the plane is -

Moment of inertia of a thin rod of mass $$M$$ and length $$L$$ about an axis passing through its center is $$\dfrac{ML^2}{12}$$. Its moment of inertia about a parallel axis at a distance of $$\dfrac{L}{4}$$ from this axis is given by

Four bodies of masses 1,2,3,4 kg respectively are placed at the corners of a square of side $$'a'$$. Coordinates of centre of mass are (take $$1\ kg$$ at origin, $$2\ kg$$ on X-axis and $$4\ kg$$ on Y-axis)

The center of mass of the dipole

A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has the velocity of 2m/s and 3kg body has 7m/s. The velocity of the centre of mass at that instant is :-

$$16\ kg$$ and $$9\ kg$$ are separated by $$25\ cm$$. The velocity with which a body should be projected from the midpoint of the line joining the two masses so that it just escape is :