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Standard :- 12
th
Subject :- Physics
Chapter1. Rotational Dynamics
MCQ’s ( 1 Mark Each)
- A diver in a swimming pool bends his head before diving. It
a) Increases his linear velocity
b) Decreases his angular velocity
c) Increases his moment of inertia
d) Decreases his moment of inertia
Ans: d) Decreases his moment of inertia
- The angular momentum of a system of particles is conserved
a) When no external force acts upon the system
b) When no external torque acts upon the system
c) When no external impulse acts upon the system
d) When axis of rotation remains the same
Ans: b) When no external torque acts upon the system
- A stone is tied to one end of a string. Holding the other end, the string is whirled in a
horizontal plane with progressively increasing speed. It breaks at some speed because
a) Gravitational forces of the earth is greater than the tension in string
b) The required centripetal force is greater than the tension sustained by the string
c) The required centripetal force is lesser than the tension in the string
d) The centripetal force is greater than the weight of the stone
Ans: b) The required centripetal force is greater than the tension sustained by the
string
- The moment of inertia of a circular loop of radius R, at a distance of R/2 around a
rotating axis parallel to horizontal diameter of the loop is
a) ½ MR
2
b) ¾ MR
2
c) MR
2
d) 2 MR
2
Ans: b) ¾ MR
2
- A 500 kg car takes a round turn of radius 50m with a velocity of 36 km/hr. The
centripetal force is
a) 250N
b) 750N
c) 1000N
d) 1200N
Ans: c) 1000N
Short Answer I (SA1) ( 2 MARKS Each )
- A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and
flies away. What will be the effect on its angular velocity?
- The moment of inertia of a uniform circular disc about a tangent in its own plane is
5/4MR
2
where M is the mass and R is the radius of the disc. Find its moment of inertia
about an axis through its centre and perpendicular to its plane.
- Derive an expression for maximum safety speed with which a vehicle should move
along a curved horizontal road. State the significance of it
- The moment of inertia of a body about a given axis is 1.2 kgm
2
. initially the body is
at rest. For what duration on angular acceleration of 25 radian/sec
2
must be applied
about that axis in order to produce a rotational kinetic energy of 1500 joule?(Ans:
t=2sec)
- A bucket containing water is tied to one end of a rope 5 m long and it is rotated in a
vertical circle about the other end. Find the number of rotations per minute in order
that the water in the bucket may not spill. ( Ans: n=13.37 rpm)
- A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The
body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the
tension in the string when the body is at the top of the circle. (Ans: T= 3.8 N)
Short Answer II (SA2) ( 3 MARKS Each )
- Derive an expression for kinetic energy of a rotating body with uniform angular
velocity.
- Obtain an expression for the torque acting on a rotating body with constant angular
acceleration.
- Derive an expression for the difference in tensions at highest and lowest point for a
particle performing vertical circular motion.
- Obtain an expression for the angular momentum of a body rotating with uniform
angular velocity.
- A railway track goes around a curve having a radius of curvature of 1 km. The
distance between the rails is 1 m. Find the elevation of the outer rail above the inner
rail so that there is no side pressure against the rails when a train goes round the curve
at 36 km / hr.(Ans: h = 1.02 cm)
- A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of
5 rad / sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm
for 10 seconds. Calculate the change in its angular momentum and change in its
kinetic energy.
(Ans: 0.1kgm
2
/s,0.625 J)
- Two wheels of moment of inertia 4 kgm
2
rotate side by side at the rate of 120 rev /
min and 240 rev / min respectively in the opposite directions. If now both the wheels
are coupled by means of a weightless shaft so that both the wheels rotate with a
common angular speed. Calculate the new speed of rotation. (Ans: n = 60 rpm)
Long Answer ( LA) ( 4 marks Each)
State and explain the theorem of parallel axes.
What is a conical pendulum? Obtain an expression for its time period
Obtain an expression for maximum safety speed with which a vehicle can be safely
driven along a curved banked road
OR
Show that the angle of banking is independent of mass of vehicle.
- Two stones with radii 1:2 fall from a great height through atmosphere. Their terminal
velocities are in the ratio
a) 2:
b) 1:
c) 4:
d) 1:
Ans: b) 1:
Very Short Answer (VSA) ( 1 MARK Each )
What is surface film?
What are cohesive forces?
What will be the shape of liquid meniscus for obtuse angle of contact?
What is the net weight of a body when it falls with terminal velocity through a viscous
medium?
- A square metal plate of area 100 cm
2
moves parallel to another plate with a velocity
of 10 cm/s, both plates immersed in water. If the viscous force is 200 dyne and
viscosity of water is 0.01 poise, what is the distance between them? (Ans: 0.05 cm )
- The relative velocity between two parallel layers of water is 8 cm/s and perpendicular
distance between them is 0.1 cm. Calculate the velocity gradient. (Ans:80 per second )
- Water rises to a height of 20 mm in a capillary tube. If the radius made 1/
rd
of its
previous value, to what height will the water now rise in the tube? (Ans: 60 mm )
Short Answer I (SA1) ( 2 MARKS Each )
State properties of an ideal fluid.
Compare streamline flow and Turbulent flow.
Define surface tension and angle of contact.
Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when
immersed in water of surface tension 7 x 10
N/m. The angle of contact between
water and glass is zero, density of water is 1000 kg/m
3
, g = 9.8 m/s
2
( Ans: h = 0.1428 m)
- A rain drop of radius 0.3 mm falls through air with a terminal velocity of 1 m/s. The
viscosity of air is 18 x 10
N-s /m
2
. Find the viscous force on the rain drop.
(Ans: F= 1.017 * 10
N)
- Two soap bubbles have radius in the ratio 2:3. Compare the works done in blowing
these bubbles.
(Ans: 4:9)
Short Answer II (SA2) ( 3 MARKS Each )
Explain the phenomena of surface tension on the basis of molecular theory.
Obtain an expression for the capillary rise or fall using forces method.
State Stoke’s law and give two factors affecting angle of contact.
Twenty seven droplets of water, each of radius 0.1 mm coalesce into a single drop.
Find the change in surface energy. Surface tension of water is 0.072 N/m.
( Ans: W= 1.628 X 10
J )
- A u-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is
held vertically and partially filled with a liquid of surface tension 49 dyne/cm and
zero angle of contact. Calculate the density of liquid, if the difference in the levels of
the meniscus is 1.25 cm. take g = 980 cm/s
2
( Ans: density of liquid = 0.8 g/ cm
3
- A rectangular wire frame of size 2 cm x 2 cm, is dipped in a soap solution and taken
out. A soap film is formed, it the size of the film is changed to 3 cm x 3 cm, Calculate
the work done in the process. The surface tension of soap film is 3 x 10
N/m.
( Ans: W= 3x 10
J )
Long Answer ( LA) ( 4 marks Each)
Derive the relation between surface energy & surface tension.
Obtain Laplace’s law of spherical membrane
Derive an expression for terminal velocity of the sphere falling under gravity through
a viscous medium.
Chapter 3. Kinetic Theory of gases and Radiation
MCQ’s ( 1 Mark Each)
- The average energy per molecule is proportional to
(a) the pressure of the gas (b) the volume of the gas
(c) the absolute temperature of the gas (d) the mass of the gas
Ans: c) the absolute temperature of the gas
Why the temperature of all bodies remains constant at room temperature?
Above what temperature all bodies radiate electromagnetic radiation?
If the density of nitrogen is 1.25 kg/m
3
at a pressure of 10
5
Pa, find the root mean square
velocity of oxygen molecules. (Ans: Vrms = 489.89 𝑚/𝑠 )
- Find kinetic energy of 3 litre of a gas at S.T.P given standard pressure is 1.013 x 10
5
N/m
2
(Ans: K.E.= 455.8 𝐽 )
- Determine the pressure of nitrogen at 0
o
C if the density of nitrogen at N.T.P. is 1.
kg/m
3
and R.M.S. speed of the molecules at N.T.P. is 489 m/s.
(Ans: 𝑃 = 99633.75 N/m)
Short Answer I (SA1) ( 2 MARKS Each )
State factors on which the amount of heat radiated by a body depends.
Show that for monoatomic gas the ratio of the two specific heats is 5:3.
Show that for diatomic gas the ratio of the two specific heats is 7:5.
Show the graphical representation of radiant power of a black body per unit range of
wavelength as a function of wavelength.
Draw neat labeled diagram of Ferry’s black body.
Compare the rate of radiation of metal body at 727
o
C and 227
o
C.
(Ans: 16)
- 1000 calories of radiant heat is incident on a body. If the body absorbs 400 calories of
heat, find the coefficient of emission of the body. (Ans: a=e=0.4)
- A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power
at given temperature.
(Ans: E = 1041.66 𝐽/𝑠 𝑚
ଶ
Short Answer II (SA2) ( 3 MARKS Each )
- Show that the root mean square speed of the molecules of gas is directly proportional
to the square root of the absolute temperature of the gas.
- Show that the average energy of the molecules of gas is directly proportional to the
absolute temperature of gas.
Calculate the ratio of two specific heats of polyatomic gas molecule.
Explain the construction and working of Ferry’s black body.
- Compare the rates of emission of heat by a blackbody maintained at 627
o
C and at 127
o
C, if the blackbodies are surrounded by an enclosure at 27
o
C. What would be the
ratio of their rates of loss of heat?
(Ans
ோ భ
ோ
మ
ଵ.ଶ଼
ଵ
- Determine the molecular kinetic energy (i) per mole (ii) per gram (iii) per molecule of
nitrogen molecules at 227
o
C, R = 8.310 J mole
K
,No = 6.03 x 10
26
moleculesKmole
1
. Molecular weight of nitrogen = 28.
(Ans
(i) K.E. per mole = 6.232 × 10
ଷ
J/mole
(ii) K.E. per kilogram = 0.225 × 10
ଷ
J/kg
(iii) K.E. per kmole = 1.048 × 10
ି ଶଷ
J)
- The velocity of three molecules, are 2 km s
, 4 km s
, 6 km s
velocity (ii) root mean square velocity.
(Ans
(i) mean square velocity, 𝑉
= 18.66 km s
(ii) root mean square velocity, 𝑉
௦
= 4.319 km s
Long Answer ( LA) ( 4 marks Each)
Explain spectral distribution of a blackbody radiation.
Derive expression for average pressure of an ideal gas.
Derive Mayer’s relation.
Chapter 4. Thermodynamics
MCQ’s ( 1 Mark Each)
- Which of the following is correct, when the energy is transferred to a system from its
environment?
(a) System gains energy (b) System loses energy
(c) System releases energy (d) system does not exchange energy
Ans: a) System gains energy
- Which of the following system freely allows exchange of energy and matter with its
environment?
(a) Closed (b) Isolated (c) Open (d) partially closed
Ans: c) Open
Short Answer I (SA1) ( 2 MARKS Each )
Draw p-V diagram of reversible process.
Draw p-V diagram of irreversible process.
Draw p-V diagram showing positive work with varying pressure.
Draw p-V diagram showing negative work with varying pressure.
Draw p-V diagram showing positive work at constant pressure.
3 mole of a gas at temperature 400 K expands isothermally from initial volume of 4
litre to final volume of 8 litre. Find the work done by the gas. (R = 8.31 J mol
K
( Ans: W = 6.919 𝑘𝐽 )
- An ideal gas of volume 2 L is adiabatically compressed to (1/10)
th
of its initial volume.
Its initial pressure is 1.01 x 105 Pa, calculate the final pressure. (Given 𝛾= 1.4)
(Ans: 𝑃
= 25.37 × 10
ହ
Explain the cyclic process.
Differentiate between reversible and irreversible process.
State the assumptions made for thermodynamic processes.
Short Answer II (SA2) ( 3 MARKS Each )
Classify and explain thermodynamic system.
Explain given cases related to energy transfer between the system and surrounding –
a. energy transferred (Q) > 0
b. energy transferred (Q) < 0
c. energy transferred (Q) = 0
- Explain the different ways through which internal energy of the system can be
changed.
Write a note on thermodynamic equilibrium.
Explain graphically (i) positive work with varying pressure, (ii) negative work with
varying pressure and (iii) positive work at constant pressure.
Write a note on free expansion.
One gram of water (1 cm
3
) becomes 1671 cm
3
of steam at a pressure of 1 atm. The
latent heat of vaporization at this pressure is 2256 J/g. Calculate the external work and
the increase in internal energy. (Ans. W = 169 J, ∆U = 2087 J)
- Calculate the fall in temperature of helium initially at 15
o
C when it is suddenly
expanded to 8 times its original volume (𝛾 = 5/3). (Ans. – 216.
o
C)
- A cylinder containing one gram molecule of the gas was compressed adiabatically
until its temperature rose from 27
o
C to 97
o
C. Calculate the work done and heat
produced in the gas (𝛾 = 1.5). (Ans. W = −11.63 × 10
ଶ
J and Q = 277 cal)
Long Answer ( LA) ( 4 marks Each)
- State first law of thermodynamics and derive the relation between the change in
internal energy (∆U), work done (W) and heat (Q).
Explain work done during a thermodynamic process.
Explain thermodynamics of isobaric process.
Explain thermodynamics of isochoric process.
Explain thermodynamics of adiabatic process.
Chapter 5. Oscillations
MCQ’s ( 1 Mark Each)
- A particle is moving in a circle with uniform speed. Its motion is
a) Periodic and simple harmonic
b) Non periodic
c) Periodic but not simple harmonic
d) Non periodic but simple harmonic
Ans: c) Periodic but not simple harmonic
- A particle is performing simple harmonic motion with amplitude A and angular
velocity . the ratio of maximum velocity to maximum acceleration is
a)
b) 1 /
c)
2
d) A /
Ans: b) 1 /
- Acceleration of a particle executing S.H.M. at its mean position.
a) Is infinity
b) Varies
c) Is maximum
d) Is zero
Ans: d) Is zero
- The acceleration due to gravity on the surface of moon is 1.7 m/s
2
. What is the time
period of a simple pendulum on the surface of moon if its time period on the surface of
earth is 3.5 s? ( g on the surface of earth = 9.8 m/s
2
( Ans: 8.40 sec )
- The total energy of a body of mass 2 kg performing S.H.M. is 40 J. Find its speed while
crossing the centre of the path.
( Ans: V = 6.324 m/s )
Derive differential equation of linear S.H.M.
Define linear S.H.M.
State any two laws of simple pendulum.
Short Answer II (SA2) ( 3 MARKS Each )
- The period of oscillation of simple pendulum increases by 20 % , when its length is
increased by 44 cm. find its initial length.
( Ans: L 1
= 1 m )
- A particle performing S.H.M. has velocities of 8 cm/s and 6 cm/s at displacements of
3 cm and 4 cm respectively. Calculate the amplitude and period of S.H.M.
( Ans: Amplitude = 5 cm, T= 3.14 sec )
- A particle performs linear S.H.M. of period 4 seconds and amplitude 4 cm. Find the
time taken by it to travel a distance of 1 cm from the positive extreme position.
( Ans: t = 0.46 sec )
- Obtain an expression for resultant amplitude of , composition of two S.H.M.’s having
same period along same path.
Define angular S.H.M. and obtain its differential equation.
Obtain the expression for the period of a magnet vibrating in a uniform magnetic field
and performing S.H.M.
Long Answer ( LA) ( 4 marks Each)
- Using differential equation of linear S.H.M., obtain an expression for acceleration,
velocity and displacement of simple harmonic motion.
Define ideal simple pendulum and obtain an expression for its periodic time.
Deduce the expression for kinetic energy, potential energy and total energy of a
particle performing S.H.M. State the factors on which total energy depends.
Chapter 6. Superposition of Waves
MCQ’s (1 Mark Each)
- A standing wave is produced on a string fixed at one end with the other end free.
The length of the string
a. must be an odd integral multiple of λ
b. must be an odd integral multiple of λ/
c. must be an odd integral multiple of λ/
d. must be an even integral multiple of λ
Ans: c) must be an odd integral multiple of λ/
- The equation of a simple harmonic progressive wave is given by,
y = 5 cos π [200t – x/150], where x and y are in cm and ‘t’ is in second. Then the
velocity of the wave is
a) 2 m/s b) 150 m/s c) 200 m/s d) 300 m/s
Ans: c) 200 m/s
- A man standing unsymmetrical position between two mountains and fires a gun. He
hears the first echo after 1.5 s and the second echo after 2.5 s. If the speed of sound
in air is 340 m/s, then the distance between the mountains will be
a. 400 m
b. 520 m
c. 640 m
d. 680 m
Ans: d) 680 m
- A set of tuning forks is arranged is ascending order of frequencies each tuning fork
gives 8 beats/s with the preceding one. If frequency of the first tuning fork is 120
Hz and the last fork is 200 Hz, then the number of tuning forks arranged will be,
a. 8
b. 9
c. 10
d. 11
Ans: d) 11
- In law of tension, the fundamental frequency of vibrating string is,
a. inversely proportional to square root of tension
b. directly proportional to the square of tension
c. directly proportional to the square root of tension
d. inversely proportional to density
Ans: c) directly proportional to the square root of tension
- The integral multiple of fundamental frequencies are
a. beats
b. resonance
c. overtones
d. harmonics
Ans: d) harmonics
- Prove that a pipe open at both end of length of 2L, has same fundamental frequency
as another pipe of closed at one end of length L.
- How the frequency of vibrating wire is affected, if the load is fully immersed in
water?
- A sonometer wire of length 1 m is stretched by a weight of 10 kg. The fundamental
frequency of vibration is 100 Hz. Determine the linear density of material of wire.
(Ans: m = 0.0025 × 10
kg/m)
Short Answer II (SA2) ( 3 MARKS Each )
- Find the amplitude of the resultant wave produced due to interference of two
waves given as,
y 1
= A
1
sin ωt, y 2
= A
2
sin (ωt + ϕ)
- Show that even as well as odd harmonics are present as overtone in modes of
vibration of string.
State and explain laws of vibrating strings.
Two wires of the same material and same cross section are stretched on a sonometer.
One wire is loaded with 1 kg and another is loaded with 9 kg. The vibrating length of
first wire is 60 cm and its fundamental frequency of vibration is the same as that of
the second wire. Calculate vibrating length of the other wire. (Ans: 3)
- The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25).
Where all quantities are in S.I. system. Find amplitude, frequency, wavelength and
velocity of wave. (Ans: Amplitude, A = 1 m Frequency n = 40 Hz Wavelength λ = 1
m, v = 40 m/sec
- A stretched sonometer wire is in unison with a tuning fork. When the length is
increased by 4%, the number of beats heard per second is 6. Find the frequency of the
fork.
(Ans: n 1 = 156 Hz)
Long Answer ( LA) ( 4 marks Each)
- Explain the formulation of stationary waves by analytical method. What are nodes
and antinodes? Show that the distance between two successive nodes or antinodes is
λ/2.
- Explain the production of beats and deduce analytically the expression for beats
frequency.
State and verify the laws of vibrating strings using sonometer.
Waves produced by two vibrators in a medium have wavelength 2 m and 2.1 m
respectively. When sounded together they produce 8 beats/second. Calculate wave
velocity and frequencies of the vibrators. (Ans: n 1
= 168 Hz)
Chapter 7. WAVE OPTICS
MCQ’s ( 1 Mark Each)
- When light travels from an optically rarer medium to an optically denser medium, the
speed decreases because of change in:
a) Wavelength
b) Frequency
c) Amplitude
d) Phase
Ans – a) Wavelength
- Light of wavelength 5000 A.U. falls on a plane reflecting surface. The frequency of
reflected light is…
a) 6 x 10
14
Hz
b) 5 x 10
14
Hz
c) 2 x 10
14
Hz
d) 1.666 x 10
14
Hz
Ans – a) 6 x 10
14
Hz
- Light follows wave nature because…
a) Light rays travel in a straight line
b) Light exhibits the phenomenon of reflection and refraction
c) Light exhibits the phenomenon of interference
d) Light causes the phenomenon of photoelectric effect
Ans – c) Light exhibits the phenomenon of interference
- Young’s double slit experiment is carried out using green, red and blue light, one
colour at a time. The fringe widths recorded are W G
, W
R
, and W B
respectively then…
a) W G
> W
B
> W
R
b) W B
> W
G
> W
R
c) W R
> W
B
> W
G
d) W R
> W
G
> W
B
Ans – d) W R
> W
G
> W
B
