System of Parti...

From a circular card board of uniform thickness and mass $$M$$, a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is $$\dfrac{Ma^2}{6}$$, the radius of the circular card board is 

$$F = a\bar i + 3\bar j + 6\bar k\,\,and\;\,\bar r = 2\bar i - 6\bar j - 12\bar k.$$ The of $$'a'$$ for which the angular momentum same,duration of day will be 

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

A canon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum $$20$$ N s making an angle $$30^o$$ with the original line of motion. The minimum momentum of the other part of shell just after the burst is?

An inverted T-shaped object is placed on a smooth horizontal floor as shown in Fig.
A force F is applied on the system as shown in Fig. The value of x so that the system performs pure translational motion is?

Two blocks of masses $$5$$kg and $$2$$kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of $$14$$ m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively.

Four identical rods are joined end to end from a square. The mass of each rod is $$M$$ and length of the rod is $$l$$. the moment of inertia of the square about the median line is 

A thin rod of length $$4\ l$$ and mass 4 m is bent at the points as shown in fig. what is moment of inertia of the rod about the axis passing through point O and perpendicular to the plane of the paper. 

The ratio$$ \frac {M}{m} $$,