System of Parti...

A spherical body of radius $$'R'$$ rolls on a horizontal surface with linear velocity $$'v'$$. Let $$L_1$$ and $$L_2$$ be the magnitudes of angular momenta of the body about centre of mass and point of contact $$P$$. Then,

Two persons A and B of weight 80 kg and 50 kg respectively are standing at opposite ends of a boat of mass 70 kg and length 2m, at rest. When they interchange their positions then the displacement of the center of mass of the boat will be

The mass per unit length of a non-uniform rod of length $$L$$ varies as $$m = \lambda x$$ where $$\lambda$$ is constant. The centre of mass of the rod will be at :

Four identical thin rods each of mass M and length l, form a  square frame. Moment of inertia of this frame about an axis through the center of the square and perpendicular to its plane is:

A body of mass 1 kg has a kinetic energy of motion 8 J. Its linear momentum is equal to:

If momenta of two particles of a system are given by $$\overrightarrow { { p }_{ 1 } } =2\hat { i } -\hat { j } +3\hat { k } $$ and $$\overrightarrow { { p }_{ 2 } } =$$ $$-\hat { i } +2\hat { j } +3\hat { k } $$, then the angle made by the direction of motion of the system with $$x$$-axis is 

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

A T joint is formed by two identical rods A and B each of mass m and length L in the X -Y plane as shown. Its moment of inertia about axis coinciding with A is 

Four thin uniform rods each of length L and mass m are joined to form a square. The moment of inertia of square about an axis along its one diagnol is 

In free space, a shell moving with velocity 60 m/s along the positive x-axis of an inertial frame, when passes the origin, explodes into two pieces of masses ratio 1 : 2. Velocity of the mass center after the explosion is