CH # 01: THE SCOPE OF PHYSICS
Q.1: Find the area of a rectangular plate having length (21.3 
0.2)cm and width (9.80 0.10)cm.
Q.2: Calculate (a) the circumference of a circle of radius 3.5 cm and (b) area of a circle of radius
4.65 cm.
Q.3: Show that the expression S = Vit + ½ at2 is dimensionally correct, when S is a co-ordinate and has unit of length, Vi is velocity, a is acceleration, and t is time.
Q.4: Suppose the displacement of a particle is related to a time according to expression S = ct3 .
What are the dimensions of the constant c.
Q.5: Estimate the number of litres of gasoline used by all Pakistan’s car each year: Given: No. of
cars in Pakistan = 500000. Average distance traveled per year by each car = 16000 km gasoline
consumption 6km/litre.
CH # 02: SCALARS AND VECTORS
Q.6: The following forces act on a particle P: F1 = 2i +
3j – 5k, F2 = -5i + j + 3k, F3 = i – 2j + 4k, F4
= 4i – 3j – 2k, measured in newtons Find (a) the resultant of the force (b) the
magnitude of the resultant force .
Q.7: If A = 3i – j – 4k, B = -2i + 4j – 3k and C = i + 2j – k, find
(a) 2A – B + 3C, (b) │A + B + C│, (c) │3A – 2B + 4C│, (d) a unit vector
parallel to 3A – 2B + 4C
Q.8: Two tugboats are towing a ship. Each exerts a force of 6000N,
and the angle between the two ropes is 60o . Calculate the resultant
force on the ship.
Q.9: The
position vectors of points P and Q are given by r1 = 2i +3j- k, r2
= 4i – 3j + 2k. Determine in terms of rectangular unit vector i, j and k
and find its magnitude.
Q.10: Prove that the vectors A = 3i + j – 2k, B = -i + 3j + 4k and
C = 4i – 2j – 6k can form the sides of a triangle. Find the length of the
medians of the triangle.
Q.11: Find the rectangular components of a vector A, 15 unit long when it form an angle with respect to +ve x-axis of (i) 50o , (ii) 130o (iii) 230o , (iv) 310o .
Q12: Two vectors 10 cm and 8 cm long form an angle of (a) 60o
(b) 90o and (c) 120o . Find the magnitude of difference
and the angle with respect to the larger vector.
Q.13: The angle between the vector A and B is 60o .
Given that │A│=│B│ = 1, calculate (a) │B - A│; (b) │B + A│
Q.14: A car weighing 10,000 N on a hill which makes an angle of 20
with the horizontal. Find the components of
car’s weight parallel and perpendicular to the road.
Q.15: Find the angle between A = 2i + 2j – k and B = 6i – 3j + 2k.
Q.16: Find the projection of the vector A = i – 2j + k onto the
direction of vector B = 4i – 4j + 7k.
Q.17: Find the angles α, β, γ which the vector A = 3i – 6j + 2k
makes with the positive x, y, z axis respectively.
Q.18: Find the work done in moving an object along a vector r = 3i
+ 2j – 5k if the applied force is F = 2i – j – k.
Q.19: Find the work done by a force of 30,000 N in moving an object
through a distance of 45 m when: (a) the force is in the direction of motion:
and (b) the force makes an angle of 40o to the direction of motion.
Find the rate at which the force is working at a time when the velocity is
2m/s.
Q.20: Two vectors A and B are such that │A│= 3, │B│= 4, and A.B =
-5, find (a) the angle between A and B (b) the length │A + B│ and │A - B│ (c)
the angle between (A + B) and (A – B)
Q.21: If A = 2i – 3j – k, B = i + 4j – 2k. Find (a) A x B (b) B x A (c) (A + B) x (A – B)
Q.22: Determine the unit vector perpendicular to the plane of A =
2i – 6j – 3k and B = 4i + 3j – k.
Q.23: Using the definition of vector product, prove the law of
sines for plane triangles of sides a, b and c.
Q.24: If r1 and r2 are the position vectors (both lie in xy plane) making angle θ1 and θ2 with the positive x-axis measured counter clockwise, find their vector product when
(i) │r1│= 4 cm θ1 = 30o │r2│=
3 cm θ2 = 90o
(ii) │r1│= 6 cm θ1 = 220o │r2│=
3 cm θ2 = 40o
(iii) │r1│= 10 cm θ1 = 20o │r2│=
9 cm θ2 = 110o
CH # 03: MOTION
Q.1: In an electron gun of a television set, an electron with an
initial speed of 103 m/s enters region where it is electrically
accelerated. It emerges out of this region after 1 micro second with speed of
4x105 m/s. What is the maximum length of the electron gun? Calculate
the acceleration.
Q.2: A car is waiting at a traffic signal and when it turns green, the car stats ahead with a constant acceleration of 2 m/s2 . At the same time a bus traveling with a constant speed of 10 m/s overtakes and passes the car. (a) How far beyond its starting point will the car overtake the bus? (b) How fast will the car be moving?
Q.3: A helicopter ascending at a rate of 12 m/s. At a height of 80m
above the ground, a package is dropped.How long does the package take to reach
the ground?
Q.4: A boy throws a ball upward from the top of a cliff with a speed of 14.7 m/s. On the way down it just misses the thrower and fall the ground 49 metres below. Find (a) How long the ball rises? (b) How high it goes? (c) How long it is in air and (d) with what velocity it strikes the ground.
Q.5: A helicopter weighs 3920 Newton. Calculate the force on it if
it is ascending up at a rate of 2 m/s2 . What will be force on
helicopter if it is moving up with the constant speed of 4 m/s?
Q.6: A bullet having a mass of 0.005 kg is moving with a speed of
100 m/s. It penetrates into a bag of sand and is brought to rest after moving
25cm into the bag. Find the deceleration force on the bullet. Also calculate
the time in which it is brought to rest.
Q.7: A car weighing 9800 N is moving with a speed of 40 km/h. On
the application of the brakes it comes to rest after traveling a distance of 50
metres. Calculate the average retarding force.
Q.8: An electron in a vacuum tube starting from rest is uniformly accelerated by an electric field so that it has a speed 6x106 m/s after covering a distance of 1.8cm. Find the force acting on the electron. Take the mass of electron as 9.1x10-31 kg.
Q.9: Two bodies A & B are attached to the ends of a string
which passes over a pulley, so that the two bodies hang vertically. If the mass
of the body A is 4.8 kg. Find the mass of body B which moves down with an
acceleration of 0.2 m/s2 . The value of g can be taken as 9.8 m/s2
.
Q.10: Two bodies of masses
10.2 kg & 4.5 kg are attached to the ends of a string which passes over a
pulley in such a way that the body of mass 10.2 kg lies on a smooth surface and
the other body hangs vertically. Find the acceleration of the bodies and
tension of the string and also the force, which the surface exerts, on the body
of mass 10.2 kg.
4. Law of Conservation of Momentum
Q.11: A 100 grams bullet is fired from a 10 kg gun with a speed of
1000 m/s. What is the speed of recoil of the gun?
Q.12: A 50 grams bullet is fired into a 10 kg block that is
suspended by a long cord so that it can swing as a pendulum. If the block is
displaced so that its centre of gravity rises by 10cm, what was the speed of
the bullet?
Q.13: A machine gun fires 10 bullets per second into a target. Each
bullet weighs 20 gm and had a speed of 1500 m/s. Find the force necessary to
hold the gun in position.
Q.14: A cyclist is going up a slope of 30o with a speed
of 3.5 m/s. If he stops pedaling, how much distance will he move before coming
to rest? (Assume the friction to be negligible).
Q.15: The engine of a motorcar moving up 45o slope with
a speed of 63 km/h stops working suddenly. How far will the car move before
coming to rest? (Assume the friction to be negligible).
Q.16: In question no. 15, find the distance that the car moves, if
it weighs 19,600N and the frictional force is 2000 N.
Q.17: In the Figure 3.22 find the acceleration of the masses and
the tension in the string.
Q.18: Two blocks are connected as shown in figure 3.23. If the
pulley and the planes on which the blocks are resting are frictionless, find
the acceleration of the blocks and the tension in the string.
Q.19: Two blocks each weighing 196N rest on planes as shown in
figure 3.24. If the planes and pulleys are frictionless, find the acceleration
and tension in the cord.
CH # 04: MOTION IN TWO DIMENSIONS
Q.1: A rescue helicopter drops a package of emergency ration to a stranded party on the ground. If the helicopter is traveling horizontally at 40 m/s at a height of 100 m above the ground, (a) where does the package strike the ground relative to the point at which it was released? (b) What are the horizontal and vertical component of the velocity of the package just before it hits the ground?
Q.2: A long-jumper leaves the ground at an angle of 20o to the horizontal and at a speed of 11m/s (a) How far does he jump? What is the maximum height reached? Assume the motion of the long jumper is that of projectile
Q.3: A stone is thrown upward from the top of a building at an angle of 30 o to the horizontal and with a initial speed of 20 m/s. If the height of building is 45 m. (a) Calculate the total time the stone in flight (b) What is the speed of stone just before it strikes the ground? (c) Where does the stone strike the ground?
Q.4 A ball is thrown in horizontal direction from a height of 10 m
with a velocity of 21 m/s (a) How far will it hit the ground from its initial
position on the ground? and with what velocity?
Q.5: A rocket is launched at an angle of 53o to the horizontal with an initial speed of 100 m/s. It moves along its initial line of motion with an acceleration of 30 m/s2 for 3s. At this time the engine falls and the rocket proceeds to move as a free body. Find (a) the maximum altitude reached by the rocket (b) its total time of flight, and (c) its horizontal range.
Q.6: A diver leaps from a tower with an initial horizontal velocity component of 7 m/s and upward velocity component of 3 m/s. find the component of her position and velocity after 1 second.
Q.7: A boy
standing 10m from a building can just barely reach the roof 12m above him when
he throws a ball at the optimum angle with respect to the ground. Find the
initial velocity component of the ball.
Q.8: A marter
shell is fired at a ground level target 500m distance with an initial velocity
of 90 m/s. What is its launch angle?
Q.9: What is the take off speed of a locust if its launch angle is 55o and its range is 0.8m?
Q.10: A car is
traveling on a flat circular track of radius 200m at 20 m/s and has a
centripetal acceleration ac = 4.5 m/s2 (a) If the mass of
the car is 1000 kg, what frictional force is required to provide the
acceleration? (b) if the coefficient of static frictions μs is 0.8,
what is the maximum speed at which the car can circle the track?
Q.11: The
turntable of a record player rotates initially at a rate of 33 rev/min and
takes 20s to come to rest (a) What is the angular acceleration of the
turntable, assuming the acceleration is constant? (b) How many rotation does
the turntable make before coming to rest? (c) If the radius of the turntable is
0.14m, what is the initial linear speed of a bug riding on the rim?(d) What is
the magnitude of the tangential acceleration of the bug at time t = 0?
Q.12: Tarzan swings on a vine of length 4m in a
vertical circle under the influence of gravity. When the vine makes an angle of
θ = 20o with the vertical, Tarzan has a speed of 5 m/s. Find (a) his
centripetal acceleration at this instant, (b) his tangential acceleration, and
(c) the resultant acceleration
CH # 05: TORQUE,ANGULAR MOMENTUM AND EQUILIBRIUM
Q.1: Locate the centre of mass of a system of particles each of
mass ‘m’, arranged to correspond in position to the six corners of a regular
(planar) hexagon.
Q.2: Find the position of centre of mass of five equal-mass
particles located at the five corners of a square-based right pyramid with
sides of length ‘’ and altitude ‘h’.
Q.3: The mass of the sun is 329.390 times the earth’s mass and the mean distance from the centre of the sun to the centre of the earth is 1.496x108 km. Treating the earth and sun as particles with each mass concentrated at the respective geometric centre, how far from the centre of the sun is the C.M (centre of mass) of the earth-sun system? Compare this distance with the mean radius of the sun (6.9960x105 km)
Q.4: A particle of mass 4 kg moves along the x-axis with a velocity v = 15t m/s, where t = 0 is the instant that the particle is at the origin.
(a) At t= 2 s , what is the angular momentum of particle about a
point P located on +ve y axis 6 m from the origin?
(b) What torque about P acts on the particle?
Q.5: A particle of mass ‘m’ is located at the vector position r and has a linear momentum vector p. The vector r and p are non zero. If the particle moves only in the x, y plane, prove that
Q.6: A light rigid rod 1m in length rotates in the xy-plane about a
pivot through the rod’s centre. Two particles of mass 2kg and 3kg are connected
to its ends. Determined the angular momentum of the system about the origin at
the instant the speed of each particle is 5m/s.
Q.7: A uniform beam of mass ‘M’ supports two masses m1 and m2. If the knife edge of the support is under the beam’s centre of gravity and m1 is at a distance ‘d’ from the centre, determine the position of m2 such that the system is balanced.
Q.10: A particle of mass 0.3 kg moves in the xy-plane. At the
instant its coordinates are (2, 4)m, its velocity is (3i + 4j)m/s. At this
instant determine the angular momentum of the particle relative to the origin.
Q.8: A uniform ladder of length and weight W = 50 N rests against a smooth vertical wall. If the coefficient of friction between the ladder and the ground is 0.40, find the minimum angle θmin such that the ladder may not slip.
Q.9: A ladder with a uniform density and a mass ‘m’ rests against a frictionless vertical wall at an angle of 60o . The lower end rests on a flat surface where the coefficient of friction (static) is 0.40. A student with a mass (M = 2m) attempts to climb the ladder. What fraction of the length ‘L’ of the ladder will the student have reached when the ladder begins to slip?
Q.11: A uniform horizontal beam of length 8m and weighing 200N is pivoted at the wall with its far end supported by a cable that makes an angle of 53o with the horizontal. If a person weighing 600N stands 2m from the wall, find the tension and the reaction force at the pivot.
CH # 06: GRAVITATION
Q.1: A 10 kg mass is at a distance of 1 m from a 100 kg mass. Find the gravitational force of attraction when (i) 10 kg mass exerts force on the 100 kg mass (ii) 100 kg mass exerts force on the 10 kg mass
Q.2: Compute gravitational acceleration at the
surface of the planet Jupiter which has a diameter as 11 times as compared with
that of the earth and a mass equal to 318 times that of earth.
Q.3: The mass of the planet Jupiter 1.9 x 1027 kg and that of the sun is 2.0 x 1030 kg.
If the average
distance between them is 7.8 x 1011 m, find the gravitational force
of the sun on Jupiter.
Q.4: The radius
of the moon is 27% of the earth’s radius and its mass is 1.2% of the earth’s
mass. Find the acceleration due to gravity on the surface of the moon. How much
will a 424N body weight there?
Q.5: What is the value of the gravitational acceleration at a distance of (i) earth’s radius above the earth’s surface? (ii) Twice earth’s radius above the earth’s surface?
Q.6: At what
distance from the center of the earth does the gravitational acceleration have
one half the value that it has on the earth’s surface?
Q.7: Compute
the gravitational attraction between two college students of mass 80 & 50
kg respectively, 2m apart from each other. Is this force worth worrying about?
Q.8: Determine
the gravitation between the proton and the electron in a hydrogen atom,
assuming that the electron describes a circular orbit with a radius of 0.53x10-10
m (mass of proton = 1.67x10-27 kg, mass of electron = 9.1x10-31
kg).
Q.9: A woman
with a mass of 45 kg is standing on a scale in an elevator. The elevator
accelerates with a constant acceleration of 1.2 m/s2 . What is the
women’s weight as measured by her in the elevator.
CH # 07: WORK, POWER AND ENERGY
Q.1: Calculate the work done by a force F specified by F = 3i + 4j + 5k in displacing a body from position B to position A along a straight path. The position vectors A & B are respectively given as rA = 2i + 5j – 2k & rB = 7i + 3j – 5k
Q.2: A 2000 kg car traveling at 20 m/s comes to rest on a level
ground in a distance of 100 m. How large is the average frictional force
tending to stop it?
Q.3: A 100-kg man is in a car traveling at 20 m/s. (a) Find his
kinetic energy. (b) The car strikes a concrete wall and comes to rest after the
front of the car has collapsed 1 m. The man is wearing a seat bell and harness.
What is the average force exerted by the belt and harness during the crash?
Q.4: When an object is thrown upward, it rises to a height ‘h’. How high is the object, in terms of h, when it has lost one-third of its original kinetic energy?
Q.5: A pump is needed to lift water through a height of 2.5 m at
the rate of 500 g/min. What must the minimum horse power of the pump be?
Q.6: A horse pulls a cart horizontally with a force of 40 lb at an
angle 30o above the horizontal and moves along at a speed of 6.0
miles/hr. (a) How much work does the horse do in 10 minutes? (b) What is the
power out put of the horse?
Q.7: A body of mass ‘m’ accelerates uniformly from rest to a speed
Vf in time tf. Show that the work done on the body as a
function of time ‘t’, in terms of Vf and tf, is .
Q.8: A rocket of mass 0.200 kg is launched from rest. It reaches a
point p lying at a height 30.0 m above the surface of the earth from the
starting point. In the process + 425 J of work is done on the rocket by the
burning chemical propellant. Ignoring air-resistance and the amount of mass
lost due to the burning propellant, find the speed Vf of the rocket
at the point P.
CH # 08: WAVE MOTION AND SOUND
Q.1: An object is connected to one end of a horizontal spring whose other end is fixed. The object is pulled to the right (in the positive x-direction) by an externally applied force of magnitude 20 N causing the spring to stretch through a displacement of 1 cm (a) Determine the value of force constant if, the mass of the object is 4 kg (b) Determine the period of oscillation when the applied force is suddenly removed.
Q.2: A body hanging from a spring is set into motion and the period
of oscillation is found to be 0.50 s. After the body has come to rest, it is
removed. How much shorter will the spring be when it comes to rest?
Q.3: A pipe has a length of
2.46 m. (a) Determine the frequencies of the fundamental mode and the first two
overtones if the pipe is open at both ends. Take υ = 344 m/s as the speed of
sound in air. (b) What are the frequencies determined in (a) if the pipe is
closed at one end? (c) For the case of open pipe, how many harmonics are
present in the normal human being hearing range (20 to 20000 Hz)?
Q.4: A standing wave is established in a 120 cm long string fixed
at both ends. The string vibrates in four segments when driven at 120 Hz (a)
Determine the wavelength (b) What is the fundamental frequency?
Q.5: Calculate the speed of sound in air at atmospheric pressure p = 1.01x105 N/m2 , taking γ = 1.40 and ρ = 1.2kg/m3 .
Q.6: A sound wave propagating in air has a frequency of 4000 Hz. Calculate the percent change in wave length when the wave front, initially in a region where T = 27o C, enters a region where the air temperature decreases to 10o C.
Q.7: The frequency of the second harmonic of an open pipe (open at
both ends) is equal to the frequency of the second harmonic of a closed pipe
(open at one end). (a) Find the ratio of the length of the closed pipe to the
length of the open pipe.(b) If the fundamental frequency of the open pipe is
256 Hz, what is the length of pipe? (Use υ = 340 m/s).
Q.8: A 256 Hz tuning fork produces four beats per second when
sounded with another fork of unknown frequency. What are two possible values
for the unknown frequency?
Q.9: An ambulance travels down a highway at a speed of 75 mi/h. Its
siren emits sound at a frequency of 400 Hz . What frequency will heard by a
person in a car traveling at 55 mi/h in the opposite direction as the car
approaches the ambulance and as the car moves away from the ambulance.
Q.10: A car has siren sounding a 2 kHz tone. What frequency will be
detected as stationary observer as the car approaches him at 80 km/h? Speed of
sound = 1200 km/h.
CH # 09: NATURE OF LIGHT
Q.1: How many fringes will pass a reference point if the mirror of a Michelson’s interferometer is moved by 0.08 mm. The wavelength of light used is 5800 Ao .
Q.2: In a double slit experiment the separation of the slits is 1.9
mm and the fringe spacing is 0.31mm at a distance of 1 metre from the slits.
Find the wavelength of light?
Q.3: Interference fringes were produced by two slits 0.25 mm apart
on a screen 150 mm from the slits. If eight fringes occupy 2.62 mm. What is the
wavelength of the light producing the fringes?
Q.4: Green light of a wavelength 5400 Ao is diffracted
by grating having 2000 line/cm. (a) Compute the angular deviation of the third
order image. (b) Is a 10th order image possible?
Q.5: Light of a wavelength 6x10-7 m falls normally on a
diffraction grating with 400 lines per mm. At what angle to the normal are the
1st , 2nd and 3rd order spectra produced?
Q.6: If a diffraction grating produced a 1st order spectrum of light of wavelength 6x10-7 m at an angle of 20o from the normal. What is its spacing and also calculate the number of lines per mm?
Q.7: Newton’s rings are formed between a lens and a flat glass
surface of wavelength 5.88x10-7 m. If the light passes through the
gab at 30o to the vertical and the fifth dark ring is of diameter 9
mm. What is the radius of the curvature of the lens?
Q.8: How far apart are the diffracting planes in a NaCl crystal for
which X-rays of wavelength 1.54 A o make a glancing angle of 15o
-54’ in the 1st order?
Q.9: A parallel beam of X-rays is diffracted by rocksalt crystal
the 1st order maximum being obtained when the glancing angle of incidence is 6
degree and 5 minutes. The distance between the atomic planes of the crystal is
2.8x10-10 m. Calculate the wavelength of the radiation.
CH # 10: GEOMETRICAL OPTICS
Q.1: An object 4 cm tall is placed near the axis of a thin
converging lens. If the focal length of the lens is 25 cm, where will the image
be formed and what will be the size of the image? Sketch the principal ray
diagram.
Q.2: A convex lens has a focal length of 10 cm. Determine the image
distances when an object is placed at the following distances from the lens. 50
cm, 20 cm, 15 cm, 10 cm and 5 cm
Q.3: Two converging lenses of focal lengths 40 cm and 50 cm are
placed in contact. What is the focal length of this lens combination? What is
the power of the combination in diopters?
Q.4: A converging lens of focal length 20 cm is placed in front of a converging lens of focal length 4 cm. What is the distance between the lenses if parallel rays entering the first lens leave the second lens as parallel rays?
Q.5: A parallel light beam is diverged by a concave lens of focal
length -12.5 cm and then made parallel once more by a convex lens of focal
length 50 cm. How far are the two lenses apart.
Q.6: Two lenses are in contact, a converging one of focal length 30
cm and a diverging one of focal length -10cm. What is the focal length and
power of the combination?
Q.7: Moon light passes through a converging lens of focal length 19 cm, which is 20.5 cm from a second converging lens of focal length 2 cm. Where is the image of the moon produced by the lens combination?
Q.8: Find the distance at which an object should be placed in front
of a convex lens of focal length 10 cm to obtain an image of double its size?
Q.9: A compound microscope has a 12 mm focal length objective and a
75 mm focal length eye piece, and the two lenses are mounted 200 mm apart. If
the final image is 225 mm from the eye piece, what is the magnification
produced?
Q.10: An astronomical telescope of angular magnification 1000 has
an objective of 15 m focal length. What is the focal length of the eye piece?
Q.11: A Galilean telescope has an objective of 120 mm focal length and an eye piece of 50 mm focal length. If the image seen by the eye is 300 mm from the eye piece, what is angular magnification?
Q.12: A compound microscope has an objective with a focal length of
10 mm and a tube 100 mm long. An image is produced 250 mm from the eye piece
when the object is 12 mm from the objective. What is the angular magnification?
Q.13: A converging lens of 4 dioptres is combined with a diverging
lens of -2 dioptres. Find the power and focal length of the combination?
Q.14: A convex lens forms image of an object on a fixed screen 20
cm from the lens. On moving the lens 60 cm towards the object, the image is
again formed on the screen. What is the focal length of the lens?
Q.15: Two converging lenses are 25 cm part. Focal length of each is
10 cm. An object is placed in front of one lens at 50 cm. Find the distance
between the object and the final image?
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