2(i) A body
starts from rest and moves with constant acceleration of 10 m/s2.How
much distance will it travel in the 4th second of its motion?
(ii) An astronomical
telescope having angular magnification 5 consists of two thin lenses 24 cm
apart. Find the power of its lenses.
(v) 271 fringes passed through
a reference point when a movable mirror of Michelson interferometer is moved by
0.08mm.Find the wavelength used in A0.
(vi) How many times in a second does a spaceship of diameter 30 m,
needed to be rotated in order to create artificial gravity?
(vii) A mass at the end of
spring oscillates with a period of 0.4 sec. Find the acceleration when the
displacement is 6 cm.
(ix) A uniform ladder having length “L” and weighing 50N rests
against a smooth vertical wall. If the co efficient of friction between ladder
and ground is 0.4, find the minimum angle such that the ladder may not slip.
(xii) A diffraction grating produces 3rd order spectrum
of light of wavelength 7000 Ao at an angle of 30o from
the normal. What is the grating element? Calculate the number of lines per cm.
(xiii)Two vectors A and B are such that |A|=4, |B|=6 and
A.B=13.5.Find the magnitude of difference of vectors and angle between A and B.
(xiv) A string 2m long and mass 0.004 kg, is stretched horizontally
by passing one end over a pulley and attaching a 1 kg mass to it. Find the
speed of the transverse waves on the string and frequency of the second
harmonic.
(xv) A 50 g bullet is fired into 10 kg wooden block that is suspended by a long cord so that it can swing as a pendulum. If the block is displaced as that its centre of gravity rises by 10 cm. What is the speed of the bullet?
2(i) If the
vector 
and 
are perpendicular to each other then find the
value ‘a’.
2(ii) Calculate
the angle of projection for which the maximum height of projectile is equal to
1/3 of its horizontal range.
2(v) A brick of
mass 2 kg is dropped from a height of 5m above the ground. What is its velocity
at a height of 3m above the ground?
2(vi) A 15 kg
block is suspended by a spring of spring constant 5 x 103 N/m.
Calculate the frequency of vibration of the block displaced from its
equilibrium position when it is released.
2(vi) An
astronomical telescope has a length of 105 cm and its magnification is 6.
Determine the power of objective and eye piece?
2(ix) A crane
lifts a load of 6000 N through a vertical distance of 15 m in 30 s. What is the
potential energy at the highest point of this operation?
2(x) A standing
wave is established in a 135 cm long string fixed at both ends. The string
vibrates in four loops when driven at 130 Hz. Determine the fundamental
frequency.
2(xi) A man
weighing 60 kg is standing on the floor of an elevator. Calculate the force
exerted by the man when the elevator is ascending at a rate of 2 m/s2.
2(xiii) A
balloon tied up with a wooden piece is moving upward with velocity of 15 m/s.At
a height of 300 m above the ground, the wooden piece is detached from the
balloon. How much time will it take to reach the ground?
2(xv) A
microscope has an objective of 12mm focal length and eye piece of 25 mm focal
length. What is the distance between the lenses? What is the magnifying power
if the object is in sharp focus when it is 15 mm from the objective?
2(ii) If 
and 
, find the unit vector perpendicular to the
plane of A and B.
2
(iv) The ratio of acceleration due to gravity inside a deep mine to that on the
surface of earth is 0.99.Find the depth of the mine, assuming that the density
of earth is uniform. Take the radius of earth as
.
2(v)
A horse pulls a cart horizontally with a force of 60 lb at an angle of 30
degrees above the horizontal and moves along at a speed of 8 miles per hour.
How much work does the horse do in 15 minutes and what is the power output of
the horse.(1 hp=550 lb-ft / sec) and (1 mile=5280 ft).
2(vi)
If the radius of 5th dark ring Newton’s ring is 3mm when light of
wavelength 5.89 x 10-7m is used, what will be the radius of
curvature of the lower surface of the lens used?
2(vii)
Show that the expression 
is dimensionally correct and find the
dimension of Kinetic Energy.
2(viii)
A boy standing 12m from a building can
just barely reach the roof 10m above him when he throws a ball at the optimum
angle with respect to the ground. Find the initial velocity component of the
ball.
2(xi) If a diffraction grating
produced a 3rd order spectrum of light of wavelength 7x10-7 m at an
angle of 30o from the normal. What is its spacing and also calculate
the number of lines per mm?
2(xii) A lens 2 cm focal length is to be used as a magnifying
glass. How far from the lens should the object be placed? What is its
magnifying power?
2(xv) A 100 cm long string vibrates into four loops at 50 Hz. The
linear density of the string is 4 x 10-4 gm/cm. Calculate the
tension in the string.
Q.2 (ii) Show that the following formulae are dimensionally correct:
(a) V = f
. (b) 
Q.2 (iii) Tarzan swings on a vine, of length 5m, in a vertical circle, under the influence of gravity. When the vine makes an angle of 30° with the Vertical, Tarzan has a speed of 4 m/s. Find:
(a) Centripetal acceleration at this instant (b) His tangential
acceleration
Q.2 (iv) A uniform ladder, of length 'L' and weight 50 N, tests
against a smooth vertical wall. If the coefficient of friction between the
ladder and the ground is 0.4, find the minimum angle 
such that the ladder may not slip.
Q.2 (v) .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 424 N body weigh there?
Q.2 (vi) A water pump is needed to lift water through a height of
2.5 m at the rate of 500 gm/minute. What will be the minimum horsepower of the
Pump?
Q.2 (vii)A moving car has a siren sounding a 2 KHz tone. What
frequency will be detected by a stationary observer as the car approaches him
at 80 km/h? (Speed of sound = 1200 km/h).
Q.2 (x) A converging lens of 4 dioptres is placed in contact with a
diverging lens of -2 dioptres. Find the power and the focal length of
combination.
Q.2 (xi) Determine the unit vector perpendicular to the plane of A = 3i + 4j -k and B =4i+3j-2k vectors.
Q.2 (xii) A car starts from rest and moves with a constant acceleration. During the 5th second of its motion, it covers a distance of 36 m. Calculate: (a) Acceleration of the car (b) Distance covered by the car during this time.
Q.2 ii) At what distance from centre of earth does the
gravitational acceleration have one third of the value that it has on the
earth's surface?
Q.2 iii) A 80 kg man runs up a hill through a height of 3m in 2 sec.
What is his average power output?
Q.2 iv) A car emitted a note of frequency 490 Hz, if the car
approaching towards a stationary listener at speed of 55 km/h, what frequency
will be detected by the listener. Take speed of sound as 334 m/s.
Q.2 v) An object moves along a straight line in a force field from
(3, 2, -6) to (14, 13, 9) when a uniform force F=4i + j + 3k acts on it. Find
the work done.
Q.2 vii) A boy whose mass is 100 kg when resting on the ground at
the equator if the radius of earth 'Re' is 6.4 x 106 m. Calculate
the centripetal acceleration and centripetal force.
Q.2 xii) Two sides of a triangle are formed by vectors A =3i + 6j
-2k and B = 4i - j + 3k . Determine the area of the triangle.
Q.2 xiii) A 100 g bullet is fired from a 10 kg gun with a speed of
1000 m/s. What is speed of recoil of the gun?
Q.2 xiv) A body hanging front a spring is set into motion and the period
of oscillation is found to be 0.5 sec. After the body has come to rest, it is
removed. How much shorter will the spring be when it comes to rest.
Q.2 xv) A parallel beam of X-rays is diffracted by rock salt
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 crystal is 2.81x10-10 m. Calculate the
wavelength of radiation.
2.i) A particle of mass 500 gm rotates in a circular orbit of
radius 25 cm at a constant rate of 1.5 revolutions per second. Find the angular
momentum with respect to centre of the orbit .
(iv) A car starts from rest and moves with a constant acceleration.
During the 4th second of its motion, it covers a distance of 24 meters.
Calculate the acceleration and the total distance covered by the car during
this time.
(vi) A string 2m long and
mass 0.004kg is stretched horizontally by passing one end over a frictionless
pulley and attaching a 1kg mass vertically to it. Find the speed of the
transverse waves on the string and the frequency of the second and fourth
harmonics to which the string will resonate.
(viii) Green light wavelength 5400 A is diffracted by grating
having 2000 lines/cm. Compute the angular deviation of the third order image.
(ix) A mortar shell is field
at a ground level target of 400 m distance with an initial velocity 85m/sec.
Calculate the maximum time to hit the target.
(x) Determine the unit
vector perpendicular to the plane containing A and B.
(xii) Calculate the
centripetal acceleration and centripetal force on a man whose mass is 80 kg
when resting on the ground at the equator if the radius of earth is 6.4 x 106
metres.
(xiii) The radius of 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.
(xiv) A pump of how much minimum horse power is needed to lift
water through a height of 2.5m at the rate of 500g/min?
(xv) A watch maker uses a magnifying glass of local length 5cm to
see the damaged spring of a watch. If he holds the glass close to the eye what
is the best position of the object? What is the linear magnification?
Q.2 (i) If 
and 
. Find the projection of A on to B.
Q.2 (ii) .The mass of the moon is approximately one eightieth
(1/80) of the earth's mass and its radius is one fourth (1/4) that of earth.
Find the acceleration due to gravity on the surface of the moon.
Q.2 (iii) A sound wave of frequency 500 Hz in air enters from a
region of temperature 25 degrees C to a region of temperature 5 degrees C.
Calculate the percent fractional change in wavelength.
Q.2 (iv) Prove that 
Q.2 (v) A horse pulls a cart
horizontally with a force of 40 N at an angle of 25 degrees above the
horizontal and moves along at a speed of 15 m/s . How much work does the horse
do in 5 minutes and what is the power output of the horse. Give your answer in
horse power (1 hp=746 W)
Q.2
(vi) A stone if dropped from the peak of a hill. It covers a distance of 30
meters in the last second of its motion. Find the height of the peak.
Q.2 (vii)
A magnifying glass of focal length 6 cm is used to see a small specimen. The
least distance of distinct vision of the observer is 25 cm. What is the
magnifying power of the lens?
Q.2
(viii) Tarzan swings on a vine, of
length 5m, in a vertical circle, under the influence of gravity. When the vine
makes an angle of 30° with the Vertical, Tarzan has a speed of 4 m/s. Find:
(a) Centripetal acceleration at this instant (b) His tangential
acceleration
Q.2 (ix) A car is waiting at a traffic signal. As it turns green,
the car starts ahead with a constant acceleration of 3 m/s2.At the
same time, a bus travelling with a constant speed of 20 m/s overtakes and
passes the car.
(a) How far beyond the starting point will the car overtake the
bus?
(b) What will be the velocity of the car at that time?
Q.2 (xv) Show that the following formulae are dimensionally
correct:
(a) V = f. (b)
Q.2 (ii) Give the dimensions of the following quantities: (a)
Torque (b) Angular momentum (c) Pressure (d) K.E
Q.2 (iii) Two vectors A and B are such that A=4 , B=6 and |A-B|=5.
Find |A+B|
Q.2(v) In a double slit experiment, eight fringes occupy 2.62mm on
a screen 145 mm away from the slits. The wave length of light is 545nm. Find
the slit separation.
Q.2 (vii) Find the velocity of sound in a gas when two waves, of
wavelengths 0.8m and 0.81, respectively, produce 4 beats per seconds.
Q.2 (viii) At what suitable angle is the maximum height of the
projectile 1/3 of its range?
Q.2 (x) How many times in a
second a spaceship of diameter 30 m needs to be rotated in order to create the
similar gravity as experienced on earth.
(xiii) A string, lm long and
of mass 0.004 kg, is stretched with a force. Calculate the force if the speed
of the wave in the string is 140m/sec.
2(vi) Determine a unit vector perpendicular to the plane of A=2i-6j
-3k and B=4i+3j-k
2(vii) A wooden block having 10 kg mass is suspended by a long cord, that can swing as a pendulum. A 50 gram bullet is fired which lodges itself into the block. Due to the impact, the centre of gravity of the block is raised by 10 cm. What was the initial speed of the bullet?
2(x) A uniform ladder having tength ‘l’ and weighing 50N,rests
against a smooth vertical wall. If the coefficient of friction between the
ladder and the ground is 0.40, find the minimum angle θ, such that the ladder
may not slip .
2 (xii) A water pump is needed to lift water through a height of 2.5 m at a rate of 500 gm / minute. Find its minimum power in horse power.
2(xiii) A note of frequency of 500 Hz is being emitted by an ambulance moving towards a listener at rest. If the listener detects a frequency of 526 Hz, calculate the speed of the ambulance. (speed of sound is 340 m/s at that moment)
2(xiv) If the diffraction grating produces first order spectrum of light of wavelength 6 x 10-7 m at an angle of 20° from the normal, calculate the number of lines per mm.
2(xv) Two converging lenses of focal lengths 30 cm and 60 cm are placed in contact. What is the focal length of this combination? Calculate the power of the combination in dioptres.
Q.2(viii) If one of the rectangular components of force 50 N is
25N; find the value of the other.
Q.2 (ix) A helicopter weight 3920 N. (a) Calculate the force on it
if It is ascending vertically at a rate of 2 m/sec2. (b) What will
be the force on the helicopter if it is moving up vertically with the constant
speed of 4 m/sec.
Q.2 (x) A water pump is needed to lift water through a height of
2.5 meters at the rate of 500 gm/minute. What will be the minimum horse power
of the pump?
Q.2 (xi) A string 2 metre long and mass 0.004 kg is stretched
horizontally by passing one of its ends over a pulley and the string is
attached with one kg mass to it vertically. Find the speed of the transverse
wave on the string and the frequency of the fundamental and fifth harmonic at
which the string will vibrate.
Q.2 (xii) A simple pendulum completes 4 vibrations in 8 seconds on
the surface of the earth. Find the time period on the surface of the moon where
the acceleration due to gravity is one-sixth that of the earth.
Q.2 (xiii) A magnifying glass produces an image of magnifying 6.
What is the power of the lens? What is the best position of the object if a
watch maker holds the same lens close to his eye to see the damaged spring of
the watch?
Q.2 (xiv) If the radius of the 14th bright Newton's ring is 1 mm
and the radius of curvature of the lens is 125 mm, calculate the wavelength of
the light.
Q.2 (xv) A uniform ladder L and weight 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.
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