fas/042/ XI/2010-11
Time: 3 Hrs.
General Instructions:
(i)
All questions are compulsory.
MM : 70
(ii)
There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9 to 18 carry two marks
each, questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each.
(iii)
There is no overall choice. However, an internal choice has been provided in one question of two marks, one
question of three marks and ONE question of five marks each. You have to attempt only one of the given
choices in such questions.
(iv)
Use of calculators is not permitted.
1. Give an example of a motion which is non oscillatory but periodic in nature.
2. A body of mass 1 kg is moving with a velocity of 3 ms-1. Find the force required to
bring it to rest in distance of 0.75 m. Why the work done by centripetal force is zero ?
3. A car and a truck are moving on a level road so that their linear momentum are equal. Which one is moving
faster?
4. Define radius of gyration.
5. W hat is the moment of inertia of a solid sphere about its diameter?
6. Write units of torque.
7. Define a quasi-static process.
8. The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from
getting too hot) should have high specific heat..
9. State Pascal's principle and describe how it is used in hydraulic lifts.
10. Explain the relation between Reynolds’s no and streamline flow.
11. Two tuning fork A and B produce 4 beats /s .On loading B with wax 6 beats /s are heard .If the quantity of wax is
reduced , the number of beats /s again becomes 4 beats/s. Find the frequency of B ,if the frequency of A is 256
Hz.
12. Find the value λ of so that the vectors A=2 i +j+ λk and B=2i-4j+2k are perpendicular to each other.
13. Two masses 8 kg and 12 kg are connected at the two ends of an inextensible string that passes over a frictionless
pulley. Find the acceleration of the masses and tension in the string when masses are released.
14. Derive
, where symbols have usual meaning.
15. Explain the dependence of speed of longitudinal waves on (a) temperature (b) humidity. 2
16. Explain the need of Laplace’s correction, then by using the same calculate the speed of sound.
17. Define resonance and plot amplitude vs time graph for the same.
18. Write two difference between moment of Inertia and mass.
19. The time of oscillation of a small drop of liquid under surface tension depends upon the density ρ, radius a and
surface tension T. Using dimensional analysis prove that the period of oscillation t α √ ρa3/T.
20. Determine that vector which when added to the resultant of A= 3i-5j+7k and B=2i+4j-3k gives unit vector along ydirection.
21. Explain why, (a). A cricketer lowers his hand while catching the ball.
(b). A gun recoils when a bullet is fired.
22. Prove that Newton's second law is the real law of motion and other two laws can be obtained from it.
23. Derive Mayer’s law of specific heats of gases.
24. Calculate the ratio of two molar specific heats of diatomic and monoatomic gases.
25. Define surface tension. Obtain the ascent formula of capillary rise.
26. Explain that the Newton’s II law is the real law and other two laws can be obtained from this.
27. Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They
start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum linear velocity?
OR
A sphere of mass m and radius R is kept on top of a rough inclined plane. Find its acceleration as it rolls down the
plane. What is the frictional force required?
28.
a) Derive the expression of total energy possessed by a system executing SHM.
b) The period of oscillating system of mass m suspended by an ideal spring is 2 sec. If an additional mass of 2kg
be suspended, the time period is increased by 1 sec. Find the value of mass m.
5
OR
a)Two aero planes A and B are approaching each other and their velocities are 108km/h and 144km/h
respectively. The frequency of the note emitted by A as heard by the passengers of B is 1170 Hz.
Calculate the frequency of the note heard by the passengers in A. Given velocity of sound =350m/s.
b) Calculate equivalent K for the following systems of spring:
29
shown in fig.
Define and derive the Bernoulli’s theorem.
Or
Define the Stoke’s law and hence derive the expression of the terminal velocity of a solid spherical object falling
through a liquid of viscosity ή.
30 Define Carnot’s theorem. By explaining all the processes in Carnot’s cycle derive the expression of the efficiency
of the Carnot’s engine.
OR
a) By drawing the relevant diagram calculate the COP of a refrigerator.
b) A Carnot’s engine has the same efficiency (i) between 100 k and 500 k (ii) T k and 900 k . Calculate T k of the sink.
(b) Will the sphere be able to roll if coefficient of friction is 0.5 and angle of inclination is 30 o?
G.P.Chouhan
Email: gpchouhan_cmm244@yahoo.co.in
1. Name a pair of physical quantities which have dimensions M L2 T-1.
2. Name a physical quantity which has no unit and no dimension
OR
A cord of negligible mass is wound round the rim of a fly wheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is
applied on the cord as shown in Fig. 7.35. The flywheel is mounted on a
horizontal axle with frictionless bearings. (a) Compute the angular acceleration of the wheel. (b) Find the work done by the
pull, when 2m of the cord is unwound. (c) Find also the kinetic energy of the
wheel at this point. Assume that the wheel starts from rest.
Define two theorems of moment of Inertia and derive any one of these.
Calculate radius of gyration for a solid sphere and a disk.
A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the
front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.
Define Carnot’s theorem. By using an indicator diagram, explain all the processes in Carnot’s engine and hence derive the
expression of its efficiency.
Explain why
(a) Two bodies at different temperatures T1 and T2 if brought in thermal contact do
not necessarily settle to the mean temperature (T1 + T2 )/2.
(b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent
the different parts of a plant from getting too hot) should have high specific
heat.
In changing the state of a gas adiabatically from an equilibrium state A to another
equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the
gas is taken from state A to B via a process in which the net heat absorbed by the
system is 9.35 cal, how much is the net work done by the system in the latter case ?
(Take 1 cal = 4.19 J)
or
(a) Explain the working of a refrigerator and hence derive its COP.
(b) A thermodynamic system is taken from an original state to an intermediate state by
the linear process shown in Fig.
Define an adiabatic process and then derive expression of work done in such a process.
Explain the need for the 2nd law of thermodynamics
What do you mean by a quasi-static process, is it possible, explain.
Name the quantity responsible for the spherical shape of a rain drop.
Calculate pressure at the bottom of a swimming pool 2 m deep that is filled with
water?
200 J of heat is communicated to 2 kg of lead. Calculate the change in temperature
of lead. (Specific heat capacity of lead = 140 J kg-1k-1)
a.
b. Describe an experiment to determine the surface tension of a liquid by capillary
rise method.
[5 marks]
(OR)
a. What are cohesive and adhesive forces.
[3 marks]
b. A spherical ball of radium 0.3 mm falls vertically through water. Find the
coefficient of viscosity of water given that terminal velocity acquired by the ball is
9.8 x 10-2 m/s, density of water is 1 x 103 kgm-3, density of ball is 1.5 x 103 kgm-3.
[5 marks]
a. Give the equation of continuity for the flow of liquids.
A policeman blows a whistle of frequency of 300Hz as a car speeds past him with
a velocity of 18Km/h .find the change in frequency when heard by the driver of
car just as he passes the policeman . velocity of sound is 340m/s
Q-22 Find the expression of time period and frequency of oscillation of liquid column in
a U-Tube on applying small pressure difference
Q-23
What amount of energy will be released if 1000 droplets of water ,each of
Diameter 10-8 coalesce to form a bigger drop ?Surface tension of water is 0.072 dynes N/m
a) Derive an expression for the elastic potential energy of stretched wire
b)Why are springs made of steel and not of copper ?
Q-11Why are strings of different thickness and materials are used in a sitar or violin ?
b)Why are there so many holes in a flute ?
Q-12A refrigerator has to transfer an average of 236 J of heat /s from temperature of –
10C to 25 C .calculate the average power consumed assuming there are no energy
losses
19.
22.
15. What force is required to stretch a steel wire of 1 cm2 cross section to double its length?( Y=2x1011 Nm-2 )
1. Determine that vector which when added to the resultant of A= 3i-5j+7k and B=2i+4j-3k gives unit vector along ydirection.
2. Write the dimensions of a/b in the relation F=a√x+bt2 where F is force, x is distance and t is time
A bullet of mass 0.04 kg moving with a speed of 90 m s-1 enters a heavy wooden block and is stopped after a distance of
60 cm. What is the average resistive force exerted by the block on the bullet?
A tuning fork of unknown frequency gives 4 beats with a tuning fork of frequency 310 Hz. It gives the same number of
beats on filling. Find the frequency of the tuning fork. 2
Define an adiabatic process. Derive the expression of work done in an adiabatic process. 3
Explain what you understand from degrees of freedom of gas molecules. Calculate γ for monatomic and diatomic
molecules.
3