System of Parti...

The radius of gyration of a solid sphere of radius $$R$$ about a certain axis is also equal to $$R$$. If $$r$$ is the distance between the axis and the centre of the sphere, then $$r$$ is equal to:

A rigid body rotates about a fixed axis with variable angular velocity equal to (a-bt) at time t where a and b are constants. The angle through which it rotates before it comes to rest is___?

The cylinders P and Q are of equal of mas and length but made of metals with densities $${\rho _P}$$ and $${\rho _Q}\,\,\left( {{\rho _P} > {\rho _Q}} \right).$$ If their moment of inertia about an axis passing through centre and normal to the circular face be $${I_P}$$ and $${I_Q}$$, then:

The reduce mass of two particles having masses m and 2 m is 

Two bodies of masses 10 kg and 2 kg are moving with velocities $$2\hat { i } -7\hat { k } +3\hat { j }\ m{ s }^{ -1 }$$ and $$-10\hat { i } +35\hat { k } -3\hat { j }\ m{ s }^{ -1 }$$ respectively. The velocity of their centre of mass is

A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the coefficient of restitution, then what will be the ration of velocity of two balls after collision?

Four identical rods are joined end to end to form a square. The mass of each rod is $$M$$. The moment of inertia of the system about one of the diagonals is:

The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $$1/2M{R}^{2}$$, then its radius of gyration about a parallel axis at a distance $$2R$$ from first axis is:

Four identical rods are joined end to end to form a square. The mass of each rod is $$M$$. The moment of inertia of the system about an axis passing through the point of intersecion of diagonals and perpendicular to the plane of the square is:

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis through speed $$ 2 rad s^{-1}$$. The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip (g=10$$ms^{-2}$$).