System of Parti...

Four uniform thin rods each of mass 1 kg and length 1 m are joined in the form of a square. If the square is rotated about axis AB, then it moment of inertia is 

Mass of thin long metal rod is $$2$$ kg and its moment of inertia about an axis perpendicular to the length of the rod and passing through its one end is $$0.5kg{m^2}$$. Its radius of gyration is:

The linear density of a thin rod of length $$1.0$$m varies as $$\lambda =2$$kg/m$$+\left(\dfrac{2kg}{m^2}\right)x$$, where x is the distance from its one end. The distance of its centre of mass from its end is?

A body of mass $$3$$ kg is thrown from ground with a speed $$10$$ m/s at an angle $$53^0$$ with horizontal. At the highest point of its path it is fragmented into three identical pieces such that one of them comes to rest. Velocity of the centre of mass just after fragmentation is

Moment of a inertia of a sphere about its diameter is $$2/5\ MR^{2}$$. What  its moment of inertia about an axis perpendicular to its two diameter and passing through their point of intersection.?

The wheel of radius $$r= 300 mm$$ rolls to the right without slipping and has a velocity $$v_0= 3 m/s$$ of its center O. The speed of the point A on the wheel for the instant represented in the figure is:-

Find the M.I of rod about (i) an axis perpendicular to the rod and passing through left end (ii)An axis through its centre of mass and perpendicular to the length whose linear density varies as $$\lambda=ax$$ where a is a positive constant and $$'x'$$ is the position of an element of the rod relative to its left end.The length of the rod is $$l$$

Find the torque of a force $$\vec{F}=-3\hat{i}+\hat{j}+5 \hat{k}$$ acting at the point $$\vec{r}=7\hat{i}+3\hat{j}+\hat{k}$$ with respect to origin:-

A bullet of mass m is fired at a certain angle $$\theta$$b with the horizontal. The bullet returns to ground after time t. Then the change in momentum of the bullet is 

In Figure  a spherical part of radius $$\frac { R } { 2 }$$ is removed from a bigger solid sphere of radius $$R$$ . Assuming uniform mass distribution, a shift in the centre of mass will be: