System of Parti...

Three identical masses each of mass $$1kg$$, are placed at the corners of an equilateral triangle of side $$l$$. Then the moment of inertia of this system about an axis along one side of the triangle is

A thin rod of linear pass density $$ \lambda $$ at right angle at its mid point $$(C)$$ and fixed to points $$A$$ and $$B$$ such that it can rotate about an axis passing through $$AB$$ .The moment of inertia about an axis passing through $$AB$$ is :

A smooth horizontal rod passes through two identical rings, each of mass $$m$$. Rings are connected to a block of same mass through two strings of length $$2l$$ and $$l$$ as shown in figure. Block is released, when block is crossing lowest point its velocity is $$2\ m/s$$, velocity of left ring is

In applying the equation for motion with uniform angular acceleration $$\omega =\omega _0+\alpha t$$ the radian measure 

A solid sphere and a hollow sphere have same mass and radius. Ratio of radius of gyration of the solid sphere to that of the hollow sphere about a tangent axis is:

Find the moment of inertia of the triangular lamina of mass M about the axis of rotation AA' shown in the figure:

A body of mass $$5\ kg$$ is acted on by a net force $$F$$ which varies with time $$t$$ as shown in graph. Then the net momentum in $$SI$$ units gained by the body at the end of $$10$$ seconds is

Two blocks of masses $$2kg$$ and $$1kg$$ respectively are tied to the ends of a strings which passes over a light frictionless pulley. The masses are held at rest at the same horizontal level and then released. The distance traversed by centre of mass in $$2 $$ seconds is:($$g=10m/s^2$$)

A triangular loop of side $$l$$ carries a current $$I$$. It is placed in a magnetic field $$B$$ such that the plane of the loop in the direction of $$B$$. The torque on the loop is:

A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular velocity of $$20\ rad/s$$. When the stretches her arms fully, the spinning speed decreases in $$10\ rad/s$$/. If $$I$$ is the initial  moment of inertia of the dancer, the new moment of inertia is