Four particles of masses $m_1 = 2m,\, m_2 = 4m,\, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square?
$2\,m$
$8\,m$
$6\,m$
None of these
The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as
The torque of the force $\overrightarrow F = (2\hat i - 3\hat j + 4\hat k\,)N$ acting at the point $\overrightarrow {r\,} = (3\hat i + 2\hat j + 3\hat k)\,m$ about the origin be
The moment of inertia of a sphere (mass $M$ and radius $R$) about it’s diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $XX'$ will be
Four masses are fixed on a massless rod as shown in Fig. The moment of inertia about the axis $P$ is about ....... $kg-m^2$
$ ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moment of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct