System of Parti...

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together:-

Moment of inertia of a thin rod of mass $$m$$ and length $$l$$ about at axis passing though a point $$l/4$$ from one and perpendicular to the rod is:

Moment of momentum is called:

The density of rod $$AB$$ increases linearly from $$A$$ to $$B$$. Its midpoint is $$O$$ and its centre of mass is at $$C$$. Four axes pass through $$A, B, O$$ and $$C$$, all perpendicular to the length of the rod. The moments of inertia of the rod about these axes are $${I}_{A}$$, $${I}_{B}$$,$${I}_{C}$$ respectively.

A rubber ball of mass $$10 gm$$ and volume $$15 cm^3$$ dipped in water to a depth of $$10 m$$. Assuming density of water uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take $$g = 980 cm/s^2$$.

Using the parallel axes theorem, find the $$M.l.$$ of a sphere of mass $$m$$ about an axis that touches it tangentially. Give that $$I_{cm}=\dfrac {2}{5}mr^{2}$$.

Find the angular momentum of a particle of mass $$m$$ describing a circle of radius $$r$$ with angular speed $$\omega$$.

Two particles $$A$$ and $$B$$ initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of $$A$$ is $$v$$ and that of $$B$$ is $$2v$$, the velocity of centre of mass of the system

A uniform rod of mass $$6M$$ and length $$6I$$ is bent to make an equilateral hexagon. Its $$M.I.$$ about an axis passing through the centre of mass and perpendicular to the place of hexagon is:

The $$M.I.$$ of a thin rod of length $$\ell$$ about the perpendicular axis through its centre is $$I$$. The $$M.I.$$ of the square structure made by four such rods about a perpendicular axis to the plane and through the centre will be :