# Q. An insulating thin rod of length $\ell$ has a x linear charge density $p(x) = \rho_0 \frac{x}{\ell}$ 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 :

JEE Main JEE Main 2019

Solution:

## $\because M = NIA$ $dq =\lambda dx \,&\, A =\pi x^{2}$ $\int dm = \int\left(x\right) \frac{\rho_{0}x}{\ell}dx . \pi x^{2}$ $M = \frac{n \rho_{0}\pi}{\ell} . \int^{\ell}_{0} x^{3} .dx = \frac{n \rho_{0} \pi}{\ell} . \left[\frac{L^{4}}{4}\right]$ $M = \frac{n\rho_{0} \pi \ell^{3}}{4}$ or $\frac{\pi}{4} n\rho\ell^{3}$

You must select option to get answer and solution

## 1. The increase in pressure required to decrease the 200 L volume of a liquid by 0.004% (in kPa) is (Bulk modulus of the liquid ==2100 MPa)

Maharashtra CET 2006 Mechanical Properties Of Solids

## 2. To draw maximum current from a combination of cells, how should the cells be grouped?

AFMC 2006 Current Electricity

AFMC 2010 Atoms

NEET 2019 Waves

## 5. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

AIPMT 1997 Gravitation

## 6. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$ . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

NEET 2017 System Of Particles And Rotational Motion

## 7. The temperature of 100 g of water is to be raised from 24°C to 90°C by adding steam to it. The mass of the steam required for this purpose is

JIPMER 2015 Thermal Properties Of Matter

## 8. The hot wire ammeter measures

Rajasthan PMT 2004 Alternating Current

## 9. The diameter of a flywheel is increased by 1%. Increase in its moment of inertia about the central axis is

JIPMER 2015 System Of Particles And Rotational Motion

## 10. A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

KCET 2008 Laws Of Motion