Physics

If the rotational kinetic energy of a body is E and moment of inertia is I then angular momentum will be:

       (A) \( EI \)        (B) \( \sqrt{2EI} \)       (C) \( \frac{E}{I} \)             (D) \( \sqrt{IE} \)

The displacement versus time graph of particles in SHM is shown in figure. The maximum velocity of the particle is

     (A) \( 1 \text{ cm s}^{-1} \)      (B) \( 0.2 \text{ cm s}^{-1} \)   (C)\( 3.14 \text{ cm s}^{-1} \)      (D)\( 31.4 \text{ cm s}^{-1} \) 

Two capillary tubes P and Q of radii 4 mm and 2  mm are dipped in water. What is the ratio of heights through which liquid rises in the tubes P and Q?

 (A) 1:2         (B) 2:1      (C) 1:4      (D) 4:1

A system undergoes an isochoric process so that its temperature changes from\( 127^\circ\text{C} \)  to \( 227^\circ\text{C} \). What is the ratio of initial pressure to final pressure?

A) \( \frac{4}{5} \)         B) \( \frac{5}{4} \)        C)\( \frac{227}{127} \)      D) \( \frac{127}{227} \)

Given figure represents the block diagram of a heat engine. What is the efficiency of this engine?

      A) 25%          B) 50%        

     C) 60%           D) 75%

What is the distance between two consecutive particles in a wave which are in the same phase?

A) \( \frac{\lambda}{4} \)     B)\( \frac{\lambda}{2} \)        C) \( \frac{3\lambda}{4} \)      D) \( \lambda \)

A polarizer is used to 

(A) reduce intensity of light                                      (B) produce diffracted light
(C) increase intensity of light                                   (D) produce unpolarized light

Which of the followings is the ferromagnetic material?
(A) Aluminium               (B) Gold                (C) Copper                   (D) Cobalt

The temperature of inversion of a thermocouple is 600°C and the neutral temperature is 310°C. What must be the temperature of cold junction?

    (A) 0°C       (B) 10°C                     (C) 20°C                  (D) 30°C

In our country Nepal, the supply ac voltage is 220V. The peak value of voltage is about

     (A) 110V               (B) 220V               (C) 310V       (D) 350V

If a P-Wave were to go from a solid to a liquid, what would happen to its velocity?
A) remains the same        B) increases
C) decreases                   D) decreases up to zero

Define the moment of inertia. 

b) A uniform rod of mass $m$ and length L is rotating about an axis AB passing through its one end and perpendicular to the length. Calculate the moment of inertia of the rod about the axis AB. 

c) A fly wheel of moment of inertia \( 0.32\text{ kgm}^2 \) is rotated steadily at 120 rad/sec by a 50 watt electric motor. Calculate: 

      i) the kinetic energy of the fly wheel.

      ii) the frictional couple opposing the rotation.

           OR

a) One end of a light spring having spring constant 18 N/m is attached to a rigid support. A mass of 0.15kg is suspended from other end of the spring. A student pulls down it such that extension of spring increases by 4cm. The student now releases it, as a result, the mass performs SHM.

i) Define simple harmonic motion.

ii) Calculate the maximum acceleration and time period of SHM. 

b) Write an expression for total energy of a particle executing SHM. Also draw a graph showing the variation of K.E. and P.E. of it.

a) Derive a relation between surface tension and surface energy. 

b) N identical spherical drops of water falling with a terminal velocity\( v_1 \) were to coalesce to form a bigger drop and fall with a new terminal velocity \( v_1 \)\( v_2 \) through air. (Neglect air resistance)

i) Obtain a relation between \( v_1 \) and \( v_1 \)

ii) If N=2 and \( v_1 = 0.4 \text{ ms}^{-1} \) then calculate \( v_2 \)

The given figure represents the P-V diagram of a cyclic process.

a) Define indicator diagram. 

 b) Estimate the workdone during II process. 

 c) Identify the thermodynamic processes represented by I, II, III and IV.

a) What correction was made by Laplace over the Newton's formula for velocity of sound in a gas? Obtain the corrected formula.

b) Calculate the wavelength of wave in air at \( 25^\circ\text{C} \) if the frequency of sound wave is \( 256 \text{ Hz} \) and velocity of sound at \( 0^\circ\text{C} \)   is   \( 330\text{ms}^{-1} \) . 

The arrangement of potentiometer circuit for the determination of internal resistance of a cell (r) is shown in figure.

Derive an expression for internal resistance of the cell.

Obtain an expression for the magnetic field intensity at any point due to a straight current carrying conductor using Ampere's circuital law. 

 A wire of length 0.5  m carrying a current of 2A is placed in a uniform magnetic field of strength 0.4T . Find the maximum and minimum force experienced by it. 

a) Explain quantization of charge. 

b) An ion of specific charge \( 4.40 \times 10^7 \text{ C/kg} \) is moving in a circular orbit in a magnetic field of flux density 0.4T with velocity of \( 3.52 \times 10^5 \text{ ms}^{-1} \). Calculate the radius of this orbit. 

c) Why are x-rays used in Millikan's oil drop experiment? 

                      OR

a) Define the terms half life and mean life of a radioactive substance. 

b) If 2 gm of a radioactive material having half life period of 50 years disintegrates, find out mean life of the given sample. 

c) Given figure represents decay graph of a radio active sample of half life 10 years. Estimate the value of T₃

What is rectification? Explain full wave rectification using two P-N junction diodes.

  For the digital circuit given below write the truth table showing the outputs A', B' and Y for all possible inputs A and B. 

a) The diagram shows a standing wave in an open organ pipe.

 i) Redraw the diagram and show the position of nodes and antinodes.              

 ii) Derive an expression for frequency of this mode. 

 b) What will be the effect of velocity of transverse wave in a stretched string if the radius of the string is doubled? 

c) A car is sounding its horn has a frequency 400Hz and travelling towards a stationary traffic post. A traffic police at the post detects the change in frequency of 60Hz when the car crosses him. Find the velocity of car if velocity of sound in air is \( 340\text{ms}^{-1} \)

                         OR

 a) How can a plane wavefront be converted into a spherical wavefront? Justify. 

b) What is interference of light? Two coherent waves, each of intensity I, are producing an interference pattern. What will be the resultant intensity at a point of

i) constructive interference and ii) destructive interference? 

c) A monochromatic light of wavelength 5890 A^o is incident normally on a diffraction grating which has 6000 lines per centimeter.

i) At what angle will the second order image be seen?  ii) Is third order image possible with this grating? 

a) A moving coil is very sensitive device to measure very small current.

i) Define voltage sensitivity of moving coil galvanometer. On which factors does it depend? 

ii) Why is magnetic field made radial in a moving coil galvanometer? 

b) State Faraday's laws of electromagnetic induction. The magnetic flux passing perpendicular to the plane of a coil is given by \( \phi = 4t^2 + 5t + 2 \), where \( \phi \)is in weber and t is in seconds. Calculate the magnitude of instantaneous emf induced in the coil when t = 3s. 

c) Derive an expression for energy stored in an inductor. 

                  OR

a) Obtain an expression for magnetic field strength at the centre of current carrying circular coil using Biot-Savart's law.

 b) A slice of indium antimonide 2.5 mm thick carries a current of 150 A. A magnetic field of flux density 0.5T, correctly applied, produces a maximum Hall voltage of 8.75  mV between the edges of the slice. Calculate the number of free charge carriers per unit volume assuming they each have a charge of \( -1.6 \times 10^{-19}\text{C} \) 

c) Derive an expression for the force exerted per unit length between two parallel current carrying conductors if currents are flowing in the same direction. Hence, define one ampere current.

a) Explain photoelectric effect and write Einstein photoelectric equation. 

 b) Obtain an expression for the velocity of an electron in the first excited state. 

c) Calculate the de-Broglie wavelength of an electron which has been accelerated through a potential difference of 300V.

[Mass of electron = 9.1 *10 ^-31  kg . Planck's constant,  h = 6.6 * 10 ^-34 JS ]