If $\vec F$ is the force acting on a particle having position vector $\vec r$ and $\vec \tau $ be the torque of this force about the origin, then
$\vec r \cdot \vec \tau = 0$ and $\vec F \cdot \vec \tau \ne 0$
$\vec r \cdot \vec \tau \ne 0$ and $\vec F \cdot \vec \tau = 0$
$\vec r \cdot \vec \tau > 0$ and $\vec F \cdot \vec \tau < 0$
$\vec r \cdot \vec \tau = 0$ and $\vec F \cdot \vec \tau = 0$
In an experiment with a beam balance an unknown mass $m$ is balanced by two known masses of $16\,kg$ and $4 \,kg$ as shown in figure. The value of the unknown mass $m$ is ......... $kg.$
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 ....... $J$.
Two disc one of density $7.2\, g/cm^3$ and the other of density $8.9\, g/cm^3$ are of same mass and thickness. Their moments of inertia are in the ratio
A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of:
Three thin metal rods, each of mass $M$ and length $L$ are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is