A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option
$\vec r.\vec \tau > 0$ and $\vec F.\vec \tau < 0$
$\vec r.\vec \tau = 0$ and $\vec F.\vec \tau = 0$
$\vec r.\vec \tau = 0$ and $\vec F.\vec \tau \ne 0$
$\vec r.\vec \tau \ne 0$ and $\vec F.\vec \tau = 0$
A flywheel is in the form of solid circular disc of mass $72\,kg$ and radius of $0.5\,m$ and it takes $70\, r.p.m.$ , then the energy of revolution approximately is ....... $J$.
Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$) is (Assume disc is of negligible mass)
A sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is
Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of mass of the particles are
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