System of Parti...

$$K$$ is the radius of gyration of a thin rod when it is rotating about an axis perpendicular to the length of the rod and is passing through it's centre. The length of that rod is :

$$ABC$$ is a right angled triangular plate of uniform thickness. The sides are such that $$AB > BC$$ as shown in the figure above. $$I_{1},I_{2},I_{3}$$ are moments of inertia about $$AB, BC$$ and $$AC$$ respectively. Then which of the following relations is correct ?

The moment of inertia of a meter scale of mass $$0.6 \  kg$$ about an axis perpendicular to the scale and located at the $$20 \  cm$$ position on the scale in $$kg\  m^{2}$$ is :

The radius of gyration of a rotating circular ring is maximum about which of the following axis of rotation:

Four particles each of mass $$m$$ are placed at the corners of a square of side length $$l$$. The radius of gyration of the system about an axis perpendicular to the square and passing through its center is:

A thin rod of mass $$M$$ and length $$L$$ is rotating about an axis perpendicular to the length of the rod and passing through its centre. If half of the total length rod that lies at one side of axis is cut and removed then the moment of inertia of remaining rod is:

A ceiling fan is rotating about its own axis with uniform angular velocity $$\omega $$. The electric current is switched off then due to constant opposing torque its angular velocity is reduced to $$\dfrac{2\omega }{3}$$ as it completes $$30$$ rotations. The number of rotations further it makes before coming to rest is :

$$K$$ is radius of gyration of a thin square plate about an axis perpendicular to the plane of plate and passing through its centre. The radius of gyration of plate about a parallel axis to the first and passing through a corner of plate is :

The moment of inertia of a flywheel is $$0.2  kgm^{2}$$ which is initially stationary. A constant external torque $$5  Nm$$ acts on the wheel. The work done by this torque during $$10  sec$$ is:

The radius of a flywheel is $$10  cm$$. It is rotated at the rate of $$25 rads^{-2}$$. When a constant force $$40  N$$ is applied on the rim of wheel along its tangent. The moment of inertia of wheel is: