System of Parti...

Calculate the radius of gyration of of a rod of mass 200 g and length 150 cm, about an axis passing its centre and perpendicular to its length.

Two particles of equal mass have co-ordinates $$(2m,4m,6m)$$ and $$(6m,2m,8m)$$. Of these one particle has a velocity $$\overrightarrow{V_{1}}=\left(2\hat{i}\right)m/s$$ and another particle has velocity $$\overrightarrow{V_{2}}=\left(4\hat{j}\right)m/s$$ at time $$t=0$$. The co-ordinate of their centre of mass at time $$t=1sec$$ will be :

Figure shows a cubical box that has been constructed from uniform metal plat of negligible thickness. The box is open at the top and has edge length $$40 /cm$$. The $$z$$ co-ordinate of the centre of mass of the box in $$cm$$, is  

Four identical rods of mass $$M=6 kg$$ each are welded at their ends to form a square and then welded to a massive ring having mass $$m = 4 k g$$ having radius $$R = 1 m$$. If the system is allowed to roll down the incline of inclination $$\theta = 30 ^ { \circ }$$, assume there is no slipping. The acceleration of the system will be

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height $$h$$. what is the speed of its centre of mass when the cylinder reaches its bottom

A pulley of radius $$2m$$ is rotated about its axis by a force $$F=(20t-5{t}^{2})$$ newton (where $$t$$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its aixs of rotation is $$10kg{m}^{2}$$ the number of rotations made by the pulley before its direction of motion if reversed, is:

A thin rod $$AB$$ of length $$l=1\ m$$ is such that its mass density increases uniformly from $$\rho$$ to $$A$$ to $$4\rho$$ at $$B$$, its total mass being $$M=30\ kg$$. The moment of inertia of the rod about the axis through $$A$$ perpendicular to $$AB$$ is:

A sphere of mass m and radius r rolls without slipping over a tunnel of width $$ d= \frac {8r}{5} $$ as shown in the figure (in the figure,the sphere rolls perpendicular to the plane of the page). The velocity of centre of mass of sphere is v directed into the plane of the page. The maximum speed of a point on the sphere is

A Three particles of masses 1 kg, 2 kg, 1 kg are at the points whose position vectors are $$\hat{i}+\hat{j}, 2\hat{i}-\hat{j}, 3\hat{i}+\hat{j}$$. The position vector of their centre of mass is : 

The velocities of different points of a uniform rod of length L at an instant is shown in the figure.The distance of a point from centre of mass of rod having zero velocity w.r.t. ground is.