Download 2009-10

FR. AGNEL SCHOOL
Gautam Nagar, New Delhi-110049
FAS/042/SECOND SEMESTER/2009-10
CLASS: XI
MM: 70
TIME :3 Hr
DATE:
1. A boat is likely to capsize if the people on the boat stand up. Why?
2. What is rotational analogue of force in linear motion?
3. Consider the processes A & B as shown in the indicator diagram. Identify adiabatic and isothermal
process from the graph.
P
B
A
V
4. Can a room be cooled by leaving the door of a refrigerator open?.
5. The distance traveled by a body is directly proportional to time. Is any external force acting on it?
6. A bob of mass 0.1 kg hung from the ceiling of a room by a string 2m long is set into oscillation.
The speed of the bob at its mean position is 1m/s. What is the trajectory of the bob if the string is
cut when the bob is (a) at one of its extreme positions (b) at its mean position.
7. Plot a graph between energy and time for damped oscillations.
8. When sand is poured on a rotating disc, what happens to the moment of inertia?
9. The surface tension of water is 72 dyne/cm. Express it in SI units.
10. The motor of an engine is rotating about its axis with an angular velocity of 100 rpm. It comes to
rest in 15 s after being switched off. Assuming constant angular deceleration, calculate the number
of revolutions made by it before it comes to rest.
11. A square metal plate of 10 cm side moves parallel to another plate with a velocity of 10 cm/s, both
the plates immersed in water. If the viscous force is 200 dyne and viscosity of water is 0.01 poise,
what is their distance apart?
Or
(a) The diameter of ball A is twicw the diameter of ball B. What will be the ratio of their terminal
velocities in water?
(b) How will the weight of the body be affected when it falls with a terminal velocity through a
viscous medium?
12. Explain why: (i) Detergents should have small angles of contact.
(ii) A drop of liquid under no external forces is always spherical in shape.
13. Show that the average kinetic energy of a gas molecule is directly proportional to the temperature
of the gas.
14. Which of the following represents periodic motion, SHM and non periodic motion? (a) rotation of
moon around the earth (b) motion of Halley’s comet (c) motion of the liquid in U- tube (d) a stone
thrown high in the air.
15. Prove that a pipe of length 2L open at both ends has the same fundamental frequency as another
pipe of length L closed at the other end. Also state whether the total sound will be identical for the
two pipes.
Or
(a) Why should two sources of sound have nearly equal frequencies for the formation of beats?
(b) A string 1m long with mass 0.1 g/cm is under a tension of 400 N. Find the fundamental
frequency.
16. Find the velocity of source of sound when the frequency appears to be (i) double (ii) half the
original frequency to a stationary observer. Velocity of sound= 330 m/s.
17. Plot the corresponding reference circle for each of the following simple harmonic motions.
Indicate the initial (t =0) position of the particle, the radius of the circle, and the angular speed of
the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every
case: (x is in cm and t is in s).
(a) x = –2 sin (3t + π/3)
(b) x = 2 cos πt
18. A train is moving with a velocity of 30 km/h due east and a car is moving with a velocity 40 km/h
of car as appears to the passenger in the train?
19. (a) A 30 kg shell is flying at 48 m/s, when it explodes. One of the part stops while the other part
flies on. Find the velocity of the latter. (b) Draw a graph showing the variation of force of friction
with the applied force.
Or
What is the acceleration of the block and trolley system shown in a Fig. if the coefficient of kinetic
friction between the trolley and the surface is 0.04? What is the tension in the string? (Take g =10 m s-2).
Neglect the mass of the string.
20. (a) Define a rigid body. (b) What is meant by the term equilibrium? (c) For the equilibrium of two
bodies two conditions need to be specified. State them.
OR
A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find the
rotational energy and the ratio of its rotational energy to its total energy.
21. Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get
reflected without any change in speed, as shown in Fig. What is (i) the direction of the force on the
wall due to each ball? (ii) the ratio of the magnitudes of impulses imparted to the balls by the wall.
22. A small trolley of mass 2 kg resting on a horizontal turn table is connected by a light spring to the
center of the table. When the turn table is set into rotation at a speed of 300rpm, the length of the
stretched spring is 40 cm. If the original length of the spring is 35 cm, determine the force
constant f the spring.
23. The velocity ‘v’ of water waves depends on the wavelength ‘λ’, density of water ‘ρ’ and the
acceleration due to gravity ‘g’. Deduce by the method of dimensions the relationship between
these quantities.
24. Using the parallelogram law of vectors, find the magnitude and direction of the resultant R in the
following diagram. Discuss cases for (i) θ = 0 (ii) θ = 90 (iii) θ = 180.
θ
25. On the basis of kinetic theory, derive an expression for the pressure exerted by an ideal gas.
26. (a) What do you understand by surface tension? Discuss molecular theory of surface tension.
(b) The ploughing of fields helps in the conservation of water in the soil. How?
27. A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the
geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat
of combustion is 4.0 × 104 J/g ?
28. (a) Derive Newton’s formula for the speed of sound in a gas. Why and what correction was
applied by Laplace in this formula?
(b) At a pressure of 105 N/m2, the volumetric strain of water is 5 x 10-5. Calculate the speed of
sound in water.
Or
The tranverse displacement of a string (clamped at its two ends) is given by
y(x, t) = 0.06 sin 23x cos (120 πt)
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 ×10–2 kg.
Answer the following :
(a) Does the function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite directions.
What is the wavelength, frequency, and speed of each wave ?
(c) Determine the tension in the string.
29. (a) What do you mean by (i) capillarity (ii) angle of contact? (b) Obtain an expression for the
ascent formula. (c) Plot a graph between height(h) of a liquid in a capillary tube and the radius (r ) of
the tube.
Or
(a) State and prove Bernoulli’s Theorem.
(b) Water flows through a horizontal pipe whose internal diameter is 2.0 cm at a speed of 1.0 m/s.
What should be the diameter of the nozzle, if the water has to emerge out with a speed of 4 m/s.
30. (a) Derive an expression for the work done in case of an adiabatic process.
(b) A gram molecule of a gas expands isothermally until the volume gets doubled. Calculate the amount of
work done and heat absorbed.
Or
a. What is meant by a heat engine? Obtain an expression for its efficiency.
b. Can you design an engine of 100 % efficiency? Explain your answer briefly.
c. The efficiency of Carnot cycle is 1/6. By lowering the temperature of the sink by 65 K it
increases to 1/3. Calculate the initial and final temperature of the sink.