System of Parti...

The ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $${I}_{AB},{I}_{BC}$$ and $${I}_{CA}$$ are the moments if inertia of the plate about AB,BC and CA respectively?

Different minerals are being mined from within the earth and multi-storeyed are being constructed. Due to this activity theoretically

A disc rolls down a plane of length $$L$$ and inclined at angle q, without slipping. its velocity on reaching the bottom will be :-

A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be :-

Initially two stable particles $$x$$ and $$y$$ start moving towards each other under mutual attraction. If at one time the velocities of $$x$$ and $$y$$ are $$V$$ and $$2V$$ respectively, what will be the velocity of centre of mass of the system?

A force $$\vec F=(2\hat i+3\hat j-5\hat k)\ N$$ acts at a point $$\vec {r}_{1}=(2\hat i+4\hat j+7\hat k)\ m$$. The torque of the force about the point $$\vec {r}_{2}=(\hat i+2\hat j+3\hat k)\ m$$ is :

Consider the following two statements:
(A) The linear momentum of a particle is independent of the frame of reference
(B) The kinetic energy of a particle is independent of the frame of reference

A thin rod of mass $$6m$$ and length $$6L$$ is bent into regular hexagon. The $$M.I$$ of the hexagon about a normal axis to its plane and through centre of system is 

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is l. Which of the following is true?

A spherically symmetric gravitational system of particles has a mass density
$$\rho =\left\{\begin{matrix} \rho_0,\ \ r\leq R \\ 0,\ \  r > R\end{matrix}\right.$$ where $$\rho_0$$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the centre of the system is represented by.