System of Parti...

Six identical particles each of mass 'm' are arranged at the corners of a regular hexagon of side length "L". If the mass of one of the particle is doubled, the shift in the center of mass is

Four masses m, 2m, 3m, & 4m, are kept on a straight line at 0, a, 2a & 3a as shown in figure. The radius of gyration of the system about axis AB is

The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36$$\%$$ . The $$\%$$ change in itsradius of gyration is 

Two objects initially some distance apart are released from rest. They move towards each other under mutual gravitational force. At some instant, speed of one of them is $$v$$ and that of other is $$v / 4$$ .Then speed of their centre of mass at this instant is: 

A solid sphere rolls down an inclined plane and its velocity at the bottom is $${ v }_{ 1 }$$. The same sphere slides down the plane (without friction) and its velocity at the bottom is $${ v }_{2 }$$. Which of the relations given below is correct?

Find the moment of inertia of three identical rods each of mass $$m$$ and length $$l$$ forming an equilateral triangle, about one of its sides

Half of the rectangular plate shown in figure is made of a material of density $$\rho _ { 1 }$$ and the other half of density $$\rho _ { 2 }$$.The length of the plate is $$L$$. Locate the centre of mass of the plate.

Three identical rods each of mass m and length $$\ell$$  are joined to form an equilateral triangle. The moment of inertia about an axis passing through one corner and perpendicular to the plane of triangle, is

Two circular plates of radii 8cm and 6cm cut from a uniform metal sheet . They are placed side by side , touching each other lying in the same plane . The position of the centre of mass of the system from the centre of the larger disc is 

A small uniform sphere of diameter d is rolling without slipping with in another static hollow sphere of inner diameter 6d, the velocity of the center of mass of the inner sphere being $${ V }_{ 0 }$$ in magnitude. The angular velocity of the smaller sphere about an axis passing through its C.M. perpendicular to its direction of motion is: