Physics I - Unit Wise Questions

1. What are non-inertial frames of reference? Define and explain centrifugal and Coriolis forces. (2+1+3)

1. What is meant by Galilean invariance? Show that distance and acceleration are invariant to Galilean transformation, velocity is not invariant. (2+1.5+1.5+2)

1. A reference frame rotates with respect to another inertial reference frame with uniform angular velocity w. The position, velocity and acceleration of a particle in the inertial frame of reference is  and  . Find the acceleration of the particle in the rotating frame of reference.

2. What are non-inertial frames of reference? Define and explain centrifugal and Coriolis forces. (2-1.2+3)

6. Show the path of one projectile as seen from another projectile will always be a straight line. (4)

6. The initial position of a particle of mass 100g is  and its initial velocity is  . A force  acts upon the particle for 5 sec. Obtain the final velocity and final position.

7. The initial positions of two particles are (-2, 0) and (0, -2) and they start simultaneously along the axes of x and y with uniform velocities 3i cm/s and 4j cm/s respectively. Obtain the vector representing the position of the 2nd particle with respect to the first as a function of time. (4)

7. A rocket is moving upwards with acceleration 3g. Calculate the effective weight of astronaut sitting in the rocket when his actual weight is 75 Kg. (4)

8. A particle of mass m is moving along a circular path in a plane show that force action on it is conservative. (4)

8. Find the height of geostationary satellite (as viewed by an observer on the earth’s surface); given g=9.8 ms^-2 on the earth’s surface, R= 6.38 x 10⁵m. (4)

9. The differential equation for a certain system is  ,find the time in which energy of the system falls to  times the initial value .(4)

1. Discuss the motion of a charged of a charged particle in an alternating electric field. (7)

7. A proton is accelerated through a potential difference 50V and then it is allowed cross a field free region 7.5m long. Find the time required to cross this distance. (4)

10.A water drop is observed to fall through gas of density 0.001 gm/cc with a constant velocity of 980 cm/rec .What is the radius of the drop?(η for the gas = 2 × 10⁻⁴poise) (4)

1. Write the law of conservation of momentum and the law of conservation of energy. Write Galilean transformation. Show that the laws of conservation of momentum and of conservation of energy are invariant under Galilean transformation. (2+1+4)

2. What do you mean by non-conservative forces? Also state an explain general law of conservation of energy. (2+2+3)

2. Consider a system with potential energy 

a. Show that force acting on the system is given by  .

b. For the system above it is given that  is translationally invariant i.e,.

Show that linear momentum of the system is conserved. (3.5 +3.5)

3. (a) Given the sum of external forces acting upon a system of particles equals zero, show that the total angular momentum remains constant.

(b) Write Gauss’s law for a system of charges in vacuum. Modify this law for the case when the some charges are in medium of dielectric constant K. (1.5+2)

6. Calculate the magnitude of centripetal force acting on a mass 100g placed at a distance 0.2m from the center of a rotating disk with 200 rpm. (4)

7. Given g = 9.81 ms² , radius of earth = 6.38 x 10⁶ m and gravitational constant (G=6.6 x 10^-11 m ³ Kg s^-2. Calculate the mass of the earth and time of revolution of a satellite in a circular orbit near the earth surface. (2+2)

8. A satellite of m is revolving around the earth in a circular orbit of radius r = R + h, where R is the radius of the earth and h is the height of the satellite above earth’s surface. Calculate the angular momentum of the satellite about the center of the earth. (4)

8. Show that the force defined by F = („2 x2 + 2xyj is conservative. (4)

3. What do you mean by a harmonic oscillator? Discuss the oscillation of diatomic molecule. Hence sketch the energy level diagram. (2+4+1)

9. The potential energy for the Vander Waals force between two atoms is given by U(X) = , where x is the distance between the atoms and a and b are positive constants. Calculate the force between the two atoms and plot it against x. (4)

9. A particle of mass 5 gm lies in a potential field V = (8x²+ 200) ergs/gm. Calculate its time period. (4)

9. A particle in Simple Harmonic Motion. Show that the total energy of the particle is constant. (4)

2. Write and explain Bernoulli’s theorem giving two practical examples. Deduce Bernoulli’s equation. (1+2+2+2)

3. a) State the assumptions made in deducing Stoke’s law for the motion of a small sphere in a viscous medium. Use dimensional arguments to derive Stoke’s law. (3.5)

b) Define dipole moment and derive expression for electric field of a dipole. (3.5)

4. (a)Discuss the analogy between liquid-flow and current-flow and hence, derive an expression for liquid-flow through capillaries in series. (4)

(b)State Gauss’s law and use it to show that excess charge of a charged conductor resides on its outer surface. (3)

10.In an experiment with Poiseuille’s apparatus the volume of water coming out per second is 8 cm3 through a tube of length 0.62 m and of uniform radius 0.5 mm. The pressure difference between the two ends of the tube is equal to 3.1 cm of Hg. You can use the Poiseuille’s formula to calculate the coefficient of viscosity   (4)

10. Calculate the mass of water flowing in 10 minutes through a tube 0.1 cm in diameter 40 cm long, if there is a constant pressure head of 20 cm of water. (11 for water = 0.0089 cgs units). (4)

10.Two horizontal capillary tubes A and B are connected together in series so that a steady stream of liquid flows through them. A is 0.4 mm in internal radius and 250 cm long while B is 0.3 mm in internal radius and 40 cm long. The pressure of the fluid is 7.5 cm of Hg above the atmospheric pressure at the entrance point of A. At the exit point of B the pressure is atmospheric (76 cm of Hg). What is the pressure at the junction of A and B? (4)

11. A water drop of radius 0.01 mm is falling through air neglecting the density of air as compared to the water, calculate the terminal velocity of the drop ( ɳ for air = 1.8 x 10^-4 CGS units) (4)

3. (a) Discuss the analogy between liquid-flow and current-flow and hence, derive an expression for liquid-flow through capillaries in series. (4)

(b) State Gauss’s law and use it to show that excess charge of a charged conductor resides on its outer surface. (3)

3. State and explain Gausses’ law. Apply it to find the field the field outside a uniformly changed sphere of radius a. (1+3+3)

4. Derive the expression for energy density in electric field. (7)

8. A charged particle moving along x — axis enters a region in which a constant electric field is along y — axis and a constant magnetic field is along z — axis. What is the condition that the net force acting on the charge is zero? (4)

11. Two small identical conducting spheres have charges of 2.0 x 10⁻⁹C and -0.5 x10⁻⁹ C, respectively. When they are placed 4 cm apart, what is the force between them? (4)

11. Two point charges have charge q1= 2.0 x 10^-8 C and q2=-0.7 x 10^-8 C respectively. The charges are placed 2 cm apart. Find force between the charges. (4)

11. Find the electric field at distance Z above the midpoint of a straight line segment of length 2L, which carries a uniform line chargeλ. (4)

12. Two point charges of and - q/2 are located at the origin and at (a, 0, 0) respectively. Find the point where electric field vanishes. (4)

12. Two parallel conducting plates are separated by the distance d and p.d.∆∅. A dielectric slab of dialectics constant K is and of uniform thickness is tightly fitted between the plates .find the electric filed in the dielectric.(4)

12. Find the electric field produced by a uniformly polarized sphere of radius R. (4)

12. An electron having kinetic energy 3.0 x 10^-17 J enters a region of space containing a uniform electric field E = 800 vm^-1 . The field is parallel to the electron’s velocity and decelerates it. How far does the electron travel before it comes to rest? (4)

13. Find the energy of a uniformly charged spherical shell of total charge 9 and radius R. (4)

13. Find the vector potential of an infinite solenoid with N turns per unit length ,radius R and current I.(4)

4. Discuss and derive the boundary conditions imposed on the field vectors  and  and at the interface of two dielectric media. (7)

4. Discuss the boundary conditions on the field vectors E and D? (3.5+3.5)

11. The screened coulomb potential   is very common in a conducting medium. Calculate the corresponding electric field and charge density. (4)

12. A plane slab of material with dielectric constant K has air on both sides. The electric field in air is E₀ and it is uniform and perpendicular to the boundaries. Find the field inside the dielectric. (4)

13. Two identical air capacitors are connected in series and the combination is maintained at a constant voltage 50v. A dielectric sheet of dielectric constant 6 and thickness equal to the sixth of the air gap is now inserted into one of the capacitors. What is the voltage across that capacitor? (4)

13. Two parallel conducting plates are separated by the distance d and potential difference ᐃψ. A dielectric slab of dielectric constant k is and of uniform thickness is tightly fitted between the plates. Find the electric field in the dielectric. (4)

14. What is the capacitance of a capacitor that can store 800 J at 800 V? Suppose the capacitor has parallel plates separated by 10^-5 m and filed with a dielectric of dielectric constant 2.2. What is the area of the plates? (4)

5. Derive the expression for energy density in the magnetic field. (7)

14. Show that magnetic field energy of a system of currents is given by  where  is current density, is vector potential and dv is the volume element. The integration is carried over volume. (4)

15. Calculate the energy density of uniform magnetic field of strength 1 Tesla in Vacuum [μ0 = 4π × 10⁻⁷h/n] (4)

15. Calculate the energy density of uniform magnetic field of strength I Tesla in vacuum. (μ₀=4πx10⁷NS² /z) (4)

5. Explain the term power and power factors .further discussion the phenomena of resonance and hence obtain quality factor. (2+2+2+1)

5. Explain the meanings of power and power factors. Further discuss the phenomena of resonance and hence obtain quality factor.

6. A proton is accelerated through a p.d. 50 and then it is allowed to cross a field free r ion 7.5m long. Find the time required to cross this distance. (4)

9. An LC circuit oscillates with a frequency of 200 Hz. The capacitance in the circuit is 10 μF. What is the value of the inductance? (4)

10. A parallel LCR circuit has L= 8mH, C= 10 μF and R= 0,5Ω. Calculate the natural frequency and quality factor. (4)

14.A capacitor C, a resistor R and a battery arc connected in series with a switch. The switch is closed at time t = 0. Set up the differential equation governing charge on the capacitor and find the charge as a function of time. (4)

14. A real capacitor C has a parallel leakage resistance R; it is connected in series with an ideal inductance L. Calculate JZI; find the approximate values at high and low frequencies assuming R is large. (2+2)

14. The series combination of a resistance R and an inductance L is put in parallel with the series combination of resistance R and capacitance C. Show that if R² = L|C the impedance is independent of frequency.(4)

15. Consider a simple RL circuit in which a sudden voltage V is applied. Discuss its transient behavior and find the current as a function of time. (4)

15. Consider a simple RL circuit in which a sudden voltage V is applied .Discuss its transient behavior and find the current as a function of time. (4)

15. A capacitor C, a resistor R and a battery of voltage V₀ are connected in series with a switch. The switch is closed at time t =0. Set up the differential equation for charge of on the capacitor and determine it as a function of time.

16. Show that the time average power dissipation in a circuit which carries an AC current . Here z is the impedance of the circuit: (4)

4. What do you mean by displacement current ?Prove    (3.5+3.5)

5. Derive ∆x E→ = _ − which constitutes one of the Maxwell’s equation. (7)

5. Use Maxwell’s equations to derive wave equation for electric and magnetic field. (7)

6. Explain the empirical basis for writing the Maxwell’s equations and write them. (7))

13. A straight metal wire of length l is moved in a magnetic field  with velocity . Consider the Lorentz force acting electrons in the wire and show that the potential difference across the wire is  (4)