Home
Class 12
PHYSICS
An insulting thin rod of length l has a ...

An insulting thin rod of length `l` has a linear charge density `rho(x)=rho_(0)(x)/(l)` on it. The rod is rotated about an axis passing through the origin (x=0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

A

`npl^(3)`

B

`pi/3npl^(3)`

C

`pi/4npl^(3)`

D

`pinpl^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`dq=pdx=p_(0)x/Ldx`
`di=(dq)/T=(p_(0)x/Ldx)/(1/n)=(p_(0)n)/Lxdx`
`dm=di.pix^(2)=(p_(0)n)/Lxdx.pix^(2)`
`m_("net")=intdm=(p_(0)npi)/Lint_(0)^(L)x^(3)dx=p_(0)npi(L^(4))/(4L)=(p_(0)npiL^(3))/4=pi/4p_(0)nL^(3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A thin rod of length L of mass M is bent at the middle point O at an angle of 60^@ . The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

Moment of inertia of a thin rod of mass m and length l about an axis passing through a point l/4 from one end and perpendicular to the rod is

A thin rod of length 4l, mass 4 m is bent at the point as shown in the figure. What is the moment of inertia of the rod about the axis passing through O and perpendicular to the plane of the paper?

An insulating rod of length I carries a charge q distrubuted uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency f about a fixed axis perpendicular to the the rod and passing through the pivot . The magnetic moment of the rod system is

The moment of inertia of thin rod of linear density lambda and length l about an axis passing through one end and perpendicular to its length is

A thin uniform rod of mass M and length L. Find the radius of gyration for rotation about an axis passing through a point at a distance of (L )/(4 ) from centre and perpendicular to rod.

Two identical rods each of mass M and length L are kept according to figure. Find the moment of inertia of rods about an axis passing through O and perpendicular to the plane of rods.