A thin wire of length $l$ and uniform linear mass density of $\rho $ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is
A thin wire of length $l$ and uniform linear mass density of $\rho $ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is
- A
$\frac{{3\rho {l^3}}}{{8{\pi ^2}}}$
- B
$\frac{{\rho {l^3}}}{{16{\pi ^2}}}$
- C
$\frac{{3\rho {l^3}}}{{8{\pi ^2r}}}$
- D
$\frac{{\rho {l^3}}}{{8{\pi ^2r}}}$
Similar Questions
A string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to ceiling. Centre of mass falls down as the disc unwinds the string. The tension in the string is
A string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to ceiling. Centre of mass falls down as the disc unwinds the string. The tension in the string is
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 ....... $kg$
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 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
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
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 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
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ $times$ that of the cone, the position of the centre of mass of the toy is given by
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ $times$ that of the cone, the position of the centre of mass of the toy is given by