System of Parti...

In the figure as shown pulley is light and massless thread is having two masses at their ends. Then the acceleration of centre of mass of two blocks is 

The ratio of the radii of gyration of a circular disc to that of circular ring, each of same mass and same radius about axes is 

A couple produces,_____

A uniform rod of length l and mass M rotating about a fixed vertical axis on a smooth horizontal table. It elastically strikes a particle placed at a distance l/3 from its axis and stops. Mass of the particle is   

A ring takes time $$t_1$$ in slipping down an inclined plane of length L, whereas it takes time $$t_2$$ in rolling down the same plane. The ratio of $$t_1$$ and $$t_2$$ is :

A rod of length I is held vertically stationary with its lower end located at a point 'P', on the horizontal plane. When the rod is released to topple about 'P', the velocity of the upper end of the rod with which it hits the ground is 

Eight point masses m that are held in a cubical array by rods of length 1 (whose masses are negligible). Find the moments of inertia of the system about the following axes 

Linear momentum of two particles are
$$20 \hat {i}+30 \hat{j}+40 \hat{k}$$unit and $$20 \hat{i}+40 \hat {j}+60 \hat {k}$$ unit. It's center of mass has the velocity $$4 \hat{i} +7 \hat{j} +10 \hat {k}$$ unit, so that mass of the system will be..... 

$$A = ( 2,3,5 ) ; B = ( - 1,3,2 ) ; C = ( \lambda , 5 , \mu )$$ are the vertices of a triangle. If the median $$AM$$ is equally inclined to the coordinate axes, then $$( \lambda , \mu ) =$$

Consider a system having two masses $$m_{1}$$ and $$m_{2}$$ in which first mass is pushed towards the center of mass by a distance $$a$$. The distance by which the second should be moved to keep the center of mass at same position is