All India Pre-Medical / Pre-Dental Entrance Examination

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AIPMT 2007 Physics Mains

Q. 1.

1. How many photons of wavelength 439 nm should strike on a perfectly reflecting surface in 1 second so that it may exert a force of 10N?
2. Can water be boiled without heating?

Sol.

1. When photon incident on perfectly reflecting surface then change in momentum per second
   Let n photons incident per second then force exerted,
2. On increasing pressure onto the surface of water in a pressure cooker its boiling point is elevated, similarly on decreasing pressure in a vessel containing water its boiling point will be lowered and water will begin to boil without supplying heat.

Q. 2.

1. When 4 amp current flows through battery from positive to negative terminal potential difference is 12V obtained when 2 amp current passes from negative to positive terminal of the battery potential difference 9V is obtained, calculate emf and internal resistance of the battery.
2. A small pulley of radius 20 cm and moment of inertia 0.32 kg m2 is used to hang a 2kg mass with the help of massless string. If this load is released then calculate acceleration of the block.

Sol.

1. In first case, cell is Charging so, V = E + Ir ;
   12 = E + 4´r …..(i)
   
   In 2nd case, cell is discharging so, V = E - Ir ;
   9 = E - 2 ´r …(ii)
   
   Subtracting (ii) from (i)
   by putting value of r in equation (ii)
2. Considering linear motion of load (2kg) 2g- T = 2a ….(i)

For rotational m otion of pulley

Q. 3.

1. Prove that for a monoatomic gas ratio of specific heat
2. Give the truth table of the following

Sol.

1. . The degree of freedom is the number of independent ways in which a molecule can have energy. Since mono-atomic gas can move linearly but cannot rotate. So it has only 3 degrees of freedom.
2. 

Truth table

Q. 4.

1. Write the difference between nuclear force and columbic force.
2. An airplane is moving horizontally with speed of 100 m/sec at height of 2000 m from ground. A small object isdetached from it and strikes the ground. Calculate the angle from vertical with which it strikes the ground.
3. Which of the following quantities have same dimensional formula? Angular momentum, impulse, energy, torque, force and moment of inertia.

Sol.

1. There are following differences between columbic force and nuclear force
   

   Coulombic force	Nuclear force
   a. Coulombic force is charge dependent b. It obeys inverse square law of distance c. The nature of coulombic force does not change with distance. d. It is weaker than nuclear force	a. Nuclear force is charge independent. b. It does not obey inverse square law but it obeys inverse law of rnwhere nis very large number. c. The nature of nuclear force changes with distance. d. It is very stronger than coulombic force.

2. The velocity of the object along vertical downward
   
   
3. While velocity along horizontal Vx = 100 m/s Let the angle made by object with vertical downward is
   
   
4. A dimensional formula of torque and that of energy is . So, both have same dimensional formula.

Q. 5.

1. From a table, a rod is hinged as shown in the figure. When the support is withdrawn calculate the acceleration of center of mass.

   

2. There are two wires each produces frequency of 500Hz. By what percentage tension in one wire is increased so that 5 beats per second can be heard?

Sol.

1. Torque on the rod about axis of rotation
   
   
   
2. 

Q. 6.

1. Find the force on conductor carrying current i as shown the figure.
2. A conducting cone is given charge q. How will the charge density and electric potential varies at different points of cone?

Sol.

1. The magnetic field at distance y from infinitely long conductor Force acting on dy length dF = idyB



2. Charge density
   Since potential on surface of any conductor is constant
   i.e.

Q. 7.

1. Equation for two waves is given as
   If amplitude and time period of
   resultant wave does not change then calculate
2. A solid sphere of radius a having charge q is placed inside spherical shell of inner radius r, outer radius R. Find potential at distance x, where r < x < R .
   

Sol.

1. 
2. V₁ = potential due to solid sphere of radius
   V₂ = potential due to inner surface of shell
   potential due to outer surface of shell
   

Q. 8.

1. In photoelectric effect a photon of wavelength is incident on metal surface of work function 2.5eV. Now emitted electrons enter in transverse magnetic field and turn in a circular path of radius 50 cm. Calculate charge of electron from the given data?
2. If temperature and magnetic field applied across paramagnetic substance are tripled, how many times intensity of magnetization of substance will change?

Sol.

1. Energy of incident light
   
2. From curie’s law
   If temperature and applied magnetic field are tripled then, i.e., unchanged

Q. 9.

1. Two coils m & n having 10 turns and 15 turns respectively are placed close to each other. When 2A current
   is passing through coil m, then flux linked in coil n is Weber per turn. If 3A current is passed through coil n then, calculate the flux linked per turn of coil m.
2. A string having tension 360N and mass /length = . It produces to consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz. Find mass of string.

Sol.

1. Flux linked through coil n
   
2. Velocity of transverse wave in string
   

Q. 10.

1. Capacitance of is charged by 6V battery. Now it is connected with inductor of 5mH. Find current in inductor when 1/3rd of total energy is magnetic.
2. An object is thrown vertically upward with some speed. It crosses 2 points p, q which are separated by h metre. If is the time between p and highest point and coming back and is the time between q and highest point and coming back, relate acceleration due to gravity , and h

Sol.

1. Initial total energy
   
2.