QUESTION BANK
PHYSICAL
WORLD AND MEASUREMENTS
Units
and Measurements
2.
If x=at+bt2, where x is in
meters and t in hours (hr), what will be the units of ‘a’ and ‘b’?
3.
How can a systematic error be
eliminated?
4.
Write the number of significant figures
in each of the following measurements:
a) 1.67X10-27
kg;
b) 0.270
cm
5.
Give approximate ratio of 1 AU and 1
light year.
6.
If f=x3, then relative error
in f would be how many times the relative error in x?
UNIT
-2 KINEMATICS
Motion
in a straight line
1.
A police van running on highway with a
speed of 30 kmh-1 fires a bullet at the thief’s car speeding away in
the same direction with a speed of 192 kmh-1. If the muzzle speed of
the bullet is 150 ms-1, with what speed does the bullet hit the
thief’s car?
2.
What is the nature of position-time
graph for a uniform motion?
3.
What does the slope of position-time
graph indicate?
4.
The position coordinate of a moving
particle is given by x=6+18t+9t2 (x in meters and t in seconds).
What is its velocity at t=2 sec.?
5.
A ball is thrown straight up. What is
its velocity and acceleration at the top?
6.
What does the slope of velocity-time
graph represent?
7.
What does the area under
acceleration-time graph represent?
8.
Draw the following graphs for an object
projected upwards with a velocity v0, which comes back to the same
point after sometime:
(i)
Acceleration versus time graph
(ii)
Speed versus time graph
(iii)
Velocity versus time graph
9.
Draw the following graphs (expected
nature only) between distance and time of an object in case of
(i)
For a body at rest
(ii)
For a body moving with uniform velocity
(iii)
For a body moving with constant
acceleration.
10.
Draw the following graphs (expected
nature only) representing motion of an object under free fall. Neglect air
resistance.
(i)
Variation of position with respect to
time.
(ii)
Variation of velocity with respect to
time.
(iii)
Variation of acceleration with respect
to time.
Motion
in a plane
1.
On an open ground, a motorist follows a
track that turns to his left by an angle of 60˚ after every 500 m. starting
from a given turn; specify the displacement of the motorist at the third, sixth
and eighth turn. Compare the magnitude of the displacement with the total path
length covered by the motorist in each case.
2.
The ceiling of a long hall is 25 m high.
What is the maximum horizontal distance that a ball thrown with a speed of 40
ms-1can go without hitting the ceiling of the hall?
3.
A
particle starts from the origin at t=0 s with a velocity of 10.0 j m/s and
moves in the x-y plane with a constant acceleration of (8.0 i + 2.0 j) ms-2.
A
particle starts from the origin at t=0 s with a velocity of 10.0 j m/s and
moves in the x-y plane with a constant acceleration of (8.0 i + 2.0 j) ms-2.
(a) At what time is the x-coordinate of the particle 16 m? What
is the y coordinate of the particle at that time?
(b) What
is the speed of the particle at that time?
(c) What
is the angle between the vectors 
X
and X?
X and X?
4.
What is the maximum vertical height to
which a cricketer can throw a ball if he can throw it to a maximum horizontal
distance of 160 m?
5.
Two bodies are projected at angles θ and
(90˚-θ) to the horizontal with the same speed. Find the ratio of their time of
flight?
6.
The maximum range of a projectile is
2/√3 times its actual range. What is the angle of projection for actual range?
7.
State parallelogram law of vector
addition. Show that resultant of two vectors
and 
inclined at an angle θ
is R=
(A2+B2+2AB cosθ )
and inclined at an angle θ
is R= (A2+B2+2AB cosθ )
8.
What is a projectile? Find its
horizontal range and show it is maximum for an angle of 45˚.
9.
Justify the statement that a uniform
circular motion is an accelerated motion.
10.
Derive an expression for the
acceleration of a body moving in a circular path of radius ‘r’ with uniform
speed ‘v’.
11.
(a)
Show that for two complementary angles of projection of the projectile
thrown with a same velocity, the horizontal ranges are equal.
(b)
For what angle of projection of the projectile, is the range maximum?
(c)
For what angle of projection of a projectile, are the horizontal range and
maximum height attained by the projectile are equal?
UNIT
-3 LAWS OF MOTION
1.
A constant force acting on a body of
mass 3 kg changes its speed from 2 m/s to 3.5 m/s in 25 s. The direction of
motion of the force remains unchanged. What is the magnitude and the direction
of the force?
2.
Two bodies of masses 10 kg and 20 kg
respectively kept on a smooth, horizontal surface are tied to the ends of the
light string. A horizontal force F=600 N is applied to (i) B (ii) A along the
direction of the string. What is the tension in the string in each case?
3.
A person sitting in the compartment of a
train moving with uniform speed throws a ball in the upward direction (i) what
path of a ball will appear to him? (ii) What to a person standing outside?
4.
Is impulse a scalar or vector quantity?
Write its SI unit?
5.
Define coefficient of limiting friction?
6.
Define angle of friction.
7.
What provides the centripetal force to a
car taking a turn on a level road?
8.
What happens to coefficient of friction,
when weight of body is doubled?
9.
What is the need of banking a circular
road?
10.
Define the term impulse. Prove that
impulse of the force is equal to the change in momentum.
11.
What is the limiting friction? State the
laws of limiting friction.
12.
Define angle of friction. Show that the
tangent of the angle of friction is equal to the coefficient of static
friction.
13.
Define limiting friction. Prove that it
is always convenient to pull a heavier body than to push it, on the surface.
14.
Derive an expression for the work done
when a body is made to slide up a rough inclined plane.
15.
Obtain an expression for the angle which
a cyclist will have to make with the vertical, while taking a circular turn.
16.
Derive a relation for an optimum
velocity of negotiating a curve by a body in a banked curve.
UNIT
-4 WORK, ENERGY AND POWER
1.
The potential energy function for a particle executing linear simple harmonic motion is given by
V(x)=kx2/2, where k is the force constant of the oscillator. For
k=0.5 N/m, the graph of V(x) versus x is shown in Fig. 6.47. Show that a
particle of total energy 1 J moving under this potential must turn back when it
reaches x=±2m.
 |
V(x)
X
2. 
A
body constrained to move along the z-axis of a coordinate system is subjected
to a constant force
= 
+
2
+3k N, where
, , k are unit vectors
along the X,Y and Z-axis of the system respectively. What is the work done by
this force in moving the body distance of 4 m along the Z-axis?
A
body constrained to move along the z-axis of a coordinate system is subjected
to a constant force = +
2 +3k N, where, , k are unit vectors
along the X,Y and Z-axis of the system respectively. What is the work done by
this force in moving the body distance of 4 m along the Z-axis?
3. An
electron and a proton are detected in a cosmic ray experiment. The first with
kinetic energy 10 keV, and the second with 100 keV. Which is faster, the
electron or the proton? Obtain the ratio of their speeds.
4. Name
the physical quantity which is expressed as force time velocity. Is it a scalar
or a vector quantity?
5. What
are conservative and non-conservative forces? Give one example of each.
6. Derive
an expression for the potential energy of an elastic stretched spring.
7. State
and prove work energy theorem.
8. Define
the terms elastic collision and inelastic collision. What is the difference
between an inelastic collision and completely inelastic collision?
9. Show
that in case of 1-D elastic collision of two bodies, the relative velocity of
separation after the collision is equal to the relative velocity of approach
before the collision.
10. Define
the terms elastic collision and inelastic collision. A lighter body collides
with a much massive body at rest. Prove that the direction of lighter body is
reserved and massive body remains at rest.
UNIT
-5 SYSTEMS OF PARTICLES & ROTATIONAL MOTION
1. In
the HCL molecule, the separation between the nuclei of the two atoms is about
1.27Å (1 Å=10-10m). Find the approximate location of the CM of the
molecule. Given that the chlorine is about 35.5 times as massive as a hydrogen
atom and nearly all the mass of an atom is concentrated in its entire nucleus.
2. Torques
of equal magnitude is applied to a hollow cylinder and a solid sphere, both
having the same mass and radius. The cylinder is free to a rotate about its
standard axis of symmetry, and the sphere is free to rotate about an axis
passing through its center. Which of the two will acquire a greater angular
speed after a given time?
3. A
rope of negligible mass is wound round a hollow cylinder of mass 3 kg and
radius 40 cm. What is the angular acceleration of the cylinder if the rope is
pulled with a force of 30 N? What is the linear acceleration of the rope?
Assume that there is no slipping.
4. Give
an example each for a body, where the center of mass lies inside the body and
outside the body.
5. What
are the factors on which the moment of inertia of a body depends?
6. Define
torque or moment of force. Give its units and dimensions.
7. Define
a couple. Show that the moment of a couple is same irrespective of the point of
rotation of a body.
8. Derive
the relation between angular momentum and torque.
9. State
the factors on which the moment of inertia of a body depends.
10. State
and prove that theorem of perpendicular axes on moment of inertia.
11. Establish
a relation between angular momentum and moment of inertia for a rigid body.
UNIT -6 GRAVITATION
1. Assuming
the earth to be a sphere of uniform mass density, how much would a body weigh
half way down to the center of the earth if it weighed 250 N on the surface?
2. A
geostationary satellite orbits the earth at a height of nearly 36,000 km from
the surface of the earth. What is the potential due to earth’s gravity at the
site of the satellite? Mass of the earth = 6 x 1024 kg and radius =
6400 km.
3. What
is the mass of a body that weighs 1 N at a place where g=9.80ms-2?
4. How
does the orbital velocity of a satellite depend on the mass of the satellite?
5. Write
the most important application of geostationary satellite.
6. How
would the value of ‘g’ change if the earth were to shrink slightly without any
change in mass?
7. Define
acceleration due to gravity. Show that gravity decreases with depth.
8. What
do you mean by gravitational potential energy of a body? Obtain an expression
for it for a body of mass m lying at distance r from the center of the earth?
9. Derive
an expression for the escape velocity of a satellite projected from the surface
of the earth.
10. State
Kepler’s law of planetary motion.
11. Obtain
an expression for the acceleration due to gravity on the surface of the earth
in terms of mass of the earth and its radius. Discuss the variation of
acceleration due to gravity with altitude, depth and rotation of the earth.
UNIT -7 PROPERTIES OF BULK MATTER
Mechanical Properties of solids
1. A
piece of copper having a rectangular cross-section of 15.2 mm x 19.1 mm is
pulled in tension with 44,500 N forces, producing only elastic deformation.
Calculate the resulting strain.
2. What
is the value of modulus of rigidity for an incompressible liquid?
3. State
Hook’s law and hence define modulus of elasticity.
4. Define
the terms stress and strain and also state their SI units. Draw the stress
versus strain graph for a metallic wire, when stretched up to the breaking
point.
5. Represent
graphically the variation of extension with load in an elastic body. On the
graph mark:
(a)
Hooke’s law region
(b)
Elastic limit
(c)
Yield point
(d)
Breaking point
6. What
is the elastic potential energy? Prove that the work done by a stretching force
to produce certain tension in a wire is
W = ½ Stretching force X extension
Mechanical Properties of fluids
1. A
50 kg girl wearing high heel shoes balances on a single heel. The heel is
circular with a diameter 1.0 cm. What is the pressure exerted by the heel on
the horizontal floor?
2. Torricelli’s
barometer used mercury. Pascal duplicated it using French wine of density 984.
Determine the height of the wine column for normal atmospheric pressure.
3. State
Pascal’s law.
4. Define
angle of contact.
5. What
are the factors on which the angle of contact depends?
6. What
happens to the surface tension when some impurity is mixed in liquid?
7. State
Pascal’s law. Explain the working of the hydraulic lift.
8. Distinguish
between streamline and turbulent flows.
9. On
the basis of Bernoulli’s principle, explain the lift of an aircraft wing.
10. Derive
excess of pressure inside an air bubble.
11. Define
coefficient of viscosity and give its SI unit. On what factors does the
terminal velocity of a spherical ball falling through a viscous liquid depend?
Derive the formula
Vt=2r2g
(ρ - ρ’)
9 η
12. State
and prove Bernoulli’s theorem. Name any two applications of Bernoulli’s
principle.
13. State
Bernoulli’s theorem. Prove that the total energy possessed by a flowing ideal
liquid is conserved, stating assumptions used.
14. (a)
Explain why sometimes the light roofs of thatched houses are blown off during
the storm.
(b)Derive
stokes’s law dimensionally.
Thermal Properties of matter
1. In
an experiment on the specific heat of a metal, a 0.20 kg block of the metal at
150˚C is dropped in copper calorimeter (of water equivalent 0.025 kg)
containing 150 cm3 of water at 27˚C. The final temperature is 40˚C.
Compute the specific heat of the metal.
2. What
is meant by coefficient of linear expansion and coefficient of cubical
expansion? Derive relationship between them.
3. Define
coefficient of thermal conductivity. Write its SI unit.
4. State
: (i) Stefan’s law and (ii) Wien’s displacement law. How will you derive Newton’s
law of cooling from Stefan’s law?
UNIT -8 THERMODYNAMICS
1.
What is the specific heat of the gas (i)
in an isothermal process and (ii) in an adiabatic process?
2.
Heat cannot flow itself from a body at
lower temperature to a body at higher temperature is a statement or consequence
of which law of thermodynamics?
3.
On what factors, the efficiency of a Carnot
engine depends?
4.
State and explain first law of
thermodynamics. Discuss its use in isothermal and adiabatic processes.
5.
Establish relation between two specific
heats of a gas. Which is greater and why?
6.
Compare between isothermal and adiabatic
processes.
7.
What is an adiabatic process? Derive
expression for the work done during such a process.
8.
Apply first law of thermodynamics to
(i) an isochoric
process
(ii) a cyclic process
(iii) an isobaric
process
9.
Explain briefly the working principle of
a refrigerator and obtain an expression for it in terms of temperature T1
of the source and T2 of the sink.
UNIT
-9 BEHAVIOR OF PERFECT GAS
AND
KINETIC THEORY OF GASES
1.
Estimate the total number of molecules
inclusive of oxygen, nitrogen, water vapour and other constituents in a room of
capacity 25 m3 at a temperature of 27˚C and 1 atm pressure.
2.
At what temperature the Crms
of an atom in an argon gas cylinder equal to the Crms of a helium
gas atom at -20˚C? Atomic mass of argon = 39.9 U and that of helium = 4.0 U.
3.
What is the mean translational K.E. of a
perfect gas molecule at temperature T?
4.
Using the law of equi partition of
energy, show that for an ideal gas having f degrees of freedom,
ϒ=1+2/f
5.
Prove that the pressure exerted by a gas
is P=1/3ρc2, where ρ is the density and c is the root mean square
velocity.
6.
What is meant by degrees of freedom?
State the law of equi partition of energy hence calculates the values of molar
specific heats at constant volume and pressure for mono atomic, and diatomic.
UNIT
-10 OSCILLATIONS AND WAVES
Oscillations
1. The
piston in the cylinder head of a locomotive has a stroke (twice the amplitude)
of 1.0 m. If the piston moves with simple harmonic motion with an angular
frequency of 200 rev/min, what is its maximum speed?
2. What
is a second’s pendulum? What is its length?
3. How
will the time period of a simple pendulum change if its length is doubled?
4. Give
the general expression for displacement of a particle undergoing S.H.M.
5. What
is the condition to the satisfied by a mathematical relation between time and
displacement to describe a periodic motion?
6. Find
an expression of the total energy of a particle executing S.H.M.
7. What
is an ideal simple pendulum? Derive an expression for its time period?
8. Derive
expressions for the kinetic and potential energies of a harmonic oscillator.
Hence show that total energy is conserved in S.H.M.
Waves
1. The
density of oxygen is 16 times the density of hydrogen. What is the relation between the speeds of
sound in two gases?
2. The
frequency of the first overtone of a closed organ pipe is same as that of the
first overtone of an open organ pipe. What is the ratio between their lengths?
3. Velocity
of sound in air at NPT is 332 m/s. What will be the velocity, when pressure is
doubled and temperature is kept constant?
4. Write
Newton’s formula for the speed of sound in air. What was wrong with this
formula? What correction was made by Laplace in this formula?
5. The
speed of longitudinal waves ‘v’ in a given medium of density ρ is given by the
formula
V
= √ϒP/ρ
Use
this formula to explain why the speed of sound in air
(a)
is independent of pressure,
(b)
Increases with temperature, and
(c)
Increases with humidity
6. Explain
Doppler Effect in sound. Obtain an expression for apparent frequency of sound
when source and listener are approaching to each other.
7. What
are beats? Prove that the number of beats produced per second by the two sound
sources is equal to the difference between their frequencies.
8. Discuss
the formation of standing waves in a string fixed at both ends and the
different modes of vibrations.
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