Calculate the stress developed inside a tooth cavity filled with copper when hot tea at tempreature of `57^@C` is drunk. You can take bdy (tooth) temperature ot be `37^@C` and `alpha = 1.7 zz 10^-5//^@C`, bulk modulus for copper ` = 140 xx 10^9 N//m^2`.

A brass wire 1.8 m long at 27^@C is held when taut with little tension between two rigid supports. If the wire is cooled to a temperature - 39^@C , what is the tension developed in the wire, if tis diameter is 2.0 mm? Coefficient of linar expansion of brass = 2.0 xx 10^5 ^@C^-1 , Young's modulus of brass = 0.91 xx 10^11 Pa .

Calculate the voltage needed to balance an oil drop carrying 10 electrons, when located between plates of a capacitor, which are 5 mm apart. Given, mass of the drop = 3xx 10^-16 kg , charge on electrno = 1.6 xx 10^-19 C and g = 9.8 m s^-2

A current of 2.4 A flows through a wire of cross-sectional area 1.5 mm^2 . Find the current density in the wire. If the wire contains 8 xx 10^28m^-3 elecrtrons per unit volume calculate the average relaxation on time. Given that charge on electron = 1.6 xx 10^-19C and mass of electron =9.1 xx 10^-31 kg.

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of mercury at that temperature ( 20^@C ) is 4.65xx10^-1 N m^-1 The atmospheric pressure is 1.01xx 10^5Pa . Also give the excess pressure inside the drop.

Calculate the ratio of electrostatic to gravitational force between two electrons placed at a certain distance in air. Given that m_e = 9.1 xx 10^31 kg, e = 1.6 xx 10^19C and G = 6.6 xx 10^17 N m^2 kg^-2

Suppose that the particle is an electron projected with velocity v_x = 2.0 xx 10^6 m s^-1 . If E between the plates separated by 0.5 cm is 9.1 xx 10^2N//C , where will the electron strike the upper plate? (|e| =1.6 xx 10^-19 C, m_e=9.1 xx 10^-31 kg.)

The electron moves around the ucelus in a hydrogen atom of radis 0.51overset(@)A , with a speed of 2xx10^5ms^-1 . Calculate the following: The magnetic moent associated with the electron take e = 1.6 xx 10^-19 C and mu_0 = 4 pi xx 10^-7 SI units.

A point charge of 5 muC is situated at the centre of a sphere of radius 0.2 m. Calculate the electric flux through its surface. Given epsilon_0 = 8.854 xx 10^-12C^2N^-1m^-2

There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by vecF = (Qq)/(r^2) hatr where the distance r is measured in cm (=10^(-2) m) , F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1es unit of charge = 1/[3] xx 10^(-9) C . The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by c = 2.99792458 xx 10^8 m/s . An approximate value of c then is c = [3] xx 10^8 m/s . Write 1 esu of charge = x C, where x is a dimensoinless number. Show that this gives 1/(4pi epsilon_0) = (10^(-9)/x^2)(N.m^2)/(C^2) with x = 1/[3] xx 10^(-9) , we have 1/(4pi epsilon_0)= [3]^2 xx 10^9 (Nm^2)/(C^2) or 1/(4pi epsilon_0)= (2.99792458)^2 xx 10^9 (Nm)^2/(C)^2 (exactly).

Two point charges 4Q and Q are separated by a distance of 1 m in air. Also calculate the electrostatic potential energy of the system of two charges, taking Q = 2 xx 10^-7C .