SECTION “A’ – (MCQs – Multiple Choice Questions)
NOTE: Attempt all questions from this Section. Choose the correct answer for each from the given options.
i. If we go up from the surface of the earth to a distance equal to the radius of the earth, the value of g will be
- ½ g
- ¼ g
- 2 g
- 4 g
ii. A body is moving along a circular path with an increasing speed possesses.
- Tangential acceleration only
- Centripetal acceleration only
- Both tangential and centripetal acceleration
- No acceleration
iii. Beats are produced due to
iv. Yellow light from a sodium lamp is used to form Newton’s rings. The central spor in Newton’s ring will be
- Neither bright nor dark
v. In an elastic collision of two bodies.
- K.E Conserved Only
- Momentum is Conserved Only
- Both K.E and momentum are Conserved
- Neither K.E nor Momentum is Conserved
vi. Two projectiles A and B are thrown up with the same speed at an angle of 60 and 30 respectively with the horizontal, then.
- The range of “A’ will be greater
- The range of “B” will be greater
- The range of “A” and “B” will be the same
- The range is independent of the angles
vii. Two perpendicular vectors having magnitudes of 4 units and 3 units are added. Their resultant has the magnitude of
- 7 Units
- 12 Units
- 25 Units
- 5 Units
viii. The dimensions of torque are
ix. The author of the book Al-Shifa was
- Al Razi
- Abu Rehan Al-Beruni
x. The centre of the mass of a system of particles.
- Always coincides with the centre of gravity
- Never coincides with the centre of gravity
- Coincides with the centre of gravity in uniform gravitational field
- Coincides with the centre of gravity in a non-uniform
xi. The number of significant figures in 0.005040 is
xii. An angle subtended at its centre by an are who length is equal to its radius is
xiii. Which of the following is a spin motion?
- The motion of a planets round the sun
- The motion of electrons round the nucleus
- The motion of the moon round the earth
- The daily rotation of the earth causing day and night
xiv. The work done by the centripetal force “F” on a body moving in a circle is zero because
- The body moves parallel to F
- The body moves opposite to F
- The body moves at right angles to F
- The centripetal and centrifugal forces balance each other
xv. In Galilean telescope, the final image is formed is
- Real and inverted
- Real and erect
- Virtual and inverted
- Virtual and erect
xvi. When the temperature of air rises, the speed of sound waves increases because
- The frequency of wave increases
- The wave length of the wave increases
- Both the frequency and wavelength increases
- Neither frequency nor wavelength increases
SECTION “B” – (Short Answer Questions)
Q.2. Answer any TEN questions from this Section. (40 Marks)
i. Define a Couple. Show that the magnitude of the moment of a couple is given by r = Fd, when the symbols have their usual meanings.
What the differences between Fresnel and Fraunhofer diffraction? Derive Bragg’s law for X-ray diffraction.
Derive the lens formula for a convex lens.
ii. State and prove the Law of Conversation of Energy for the free fall motion.
State and prove the Law of Conversation of Momentum.
Define “wave front”. State and explain Huygen’s principle.
What are stationary waves? On what faders does the frequency of stationary waves in a stretched string depend?
iii. Establish Work-Energy Equation for a freely falling body in a gravitational field.
What are the conditions of Simple Harmonic Motion (S.H.M)? Show that the motion of a particle in a uniform Circular Motion is simple harmonic on one of its diameters of reference circle.
Define Intensity of sound and Loudness. Give Weber Fechner’s Law and explain the intensity level with its unit.
iv. Describe the addition of vectors by rectangular components methods.
Explain the cross-product of two vectors. Show that the magnitude of the vector product gives the area of the parallelogram represented by the two vectors.
v. Derive an expression for the acceleration of a body moving down an inclined plane when there is friction “f”.
Define a conservative field. Show that the gravitational field is a conservative field.
Define Projectile Motion. A projectile is thrown upward in air at an angle “?” with the horizontal with the velocity “V?”, derive the expression for the time taken to reach maximum height and horizontal range.
vi. Is it possible for a body to have an acceleration when it is moving with constant velocity or constant speed.
Define Angular Velocity and Angular Acceleration. Show that V = rw and a = r?, when the symbols have their usual meanings.
vii. Define Simple Harmonic Motion (S.H.M). Prove that the motion of Simple Pendulum is simple harmonic motion.
Write down the expression for the acceleration representing simple harmonic motion. Would you keep the amplitude of a simple pendulum small or large? Why?
viii. A boy throws a ball upward from the top of a tower with a speed of 12m/s. On the way down it just misses the thrower and falls to the ground 50m below. Find how long the ball remains in the air.
ix. How did Thomas Young achieve the condition of phase coherence for light in his double slit experiment?
What are Newton’s Rings? Derive an expression for the wavelength of light used in Newton’s Rings.
What is a Magnifying Glass? Give its working and derive an expression for its magnifying power.
x. Interference fringes were produced by two slits 0.25mm apart on a screen 150mm apart from the slits. If ten fringes occupy 3.27mm, what is the wavelength of the light producing fringes?
If a diffraction grating produces a first order spectrum of light wavelength 6 x 10??m at an angle of 20° fro the normal; calculate the number of lines per mm.
271 fringes pass a reference point when the moveable mirror of Michelson’s interferometer is moved by 0.08mm. Find the wavelength of the light in angstrom.
xi. A compound microscope has an objective with a focal length of 10mm and a tube 232mm long. The final image is produced 250mm from the eye-piece when the object is 10.5mm from the objective. What is the angular magnification.
If the magnification of a telescope is 11 and its length is 120cm, determine the focal lengths of its objective eye-piece when the telescope is focused for infinity.
xii. A wooden ball of mass 100gm is suspended by a thread. The horizontal current of air blows it one side such that the thread makes an angle of 30° with the vertical find the tension in the thread and the force of air current.
What is the take-off speed of a locust if its launching angle is 55° and its range is 0.8m? When sin 110° = 0.9397.
xiii. A rocket is fired at a ground-level target 600m away with an initial velocity 85m/s, find the two possible values of the launch angle. Calculate the minimum time to hit this target.
Calculate the centripetal acceleration acting on a man whose mass 64kg when he is resting on the ground at the equator (Radius of earth = 6.4 x 10?m).
A 150gm bullet is fired from a 15kg gun with a speed of 1000m/s. What the speed of the recoil of the gun.
xiv. A body of mass 31gm attached to an elastic spring is performing SHM. Its velocity is 0.4m/s when the displacement is 8cm towards right. If the spring constant 0.4Nm?1, calculate (a) total energy, (b) the amplitude of its motion.
The time period of a pendulum is 2 seconds at the surface of the earth calculate its time period on the surface of the moon where the value of acceleration due to gravity is one-sixth that of the value of “g” at the surface of the earth.
xv. A car has its siren sounding 2K Hz tone. If the frequency heard by a stationary listener is 2143Hz; find the speed with which it approaches the stationary listener (The speed of sound is 332m/s).
In a sonometer a wire of length 1m when plucked at the centre vibrates with a frequency 250Hz, calculate the wavelength and the speed of moves in the wire.
SECTION “C” – (Detailed Answer Questions)
NOTE: Answer any TWO questions from this Section. All questions carry equal marks. (28 Marks)
Q.3. (a) Draw a labelled diagram showing the passage of light rays through an astronomical telescope focused for infinity and obtain expression for its magnifying power.
Draw a ray diagram of a Compound Microscope and describe its construction and working. Also derive the expression for its magnification.
Q.3. (b) What is Diffraction Grating? How is it used to determine the wavelength as Sodium light? Derive the relevant mathematical expression.
Describe the experimental arrangement for observing Newton’s rings. Derive an expression for the Nth bright ring.
Q.3. (c) What is meant by interference in thin films? Obtain expressions for constructive and desctructive interference.
With the help of a ray diagram describe the construction and working of Michelson’s Interferometer.
Two thin lenses f1 and f2 placed in contact, derive the formula of the focal length of the combination.
What are the defects in lenses? How are they removed?
Q.4. (a) How is artificial gravity created in an orbiting? Derive the relevant expression.
What is the cause of weightlessness in a satellite orbiting round the earth? Show that a block suspended from the ceiling of an elevator through a spring balance will become weightless if the cable holding the elevator suddenly breaks.
Q.4. (b) What are Stationary or Standing Waves? A string of length “l” is stretched between two hooks; find the frequency of the Stationary waves when it is vibrating in (a) One loops (b) Two loops (c) Three loops (d) n loops.
Show that the total energy of a body attached to an elastic spring and executing S.H.M remains some everywhere.
Q.4. (c) Two bodies of unequal masses are attached to the ends of a string which passes over a frictionless pulley. If they are hung vertically, derive the expressions for the tension in the string and the acceleration of the bodies when the mass-string system is in motion.
What is meant by Equilibrium? Define its types. Explain the two conditions of equilibrium with mathematical expressions.
Derive expressions for variation of “g” with altitude and depth.
Q.5. (a) State Newton’s law of Gravitation. Using this law, obtain a reaction for the average Mass and average Density of the earth.
Q.5. (b) What is Doppler’s Effect? Obtain an expression for the apparent frequency heart by a listener when he moves with a velocity “V” towards a stationary source of sound emitting sound waves of frequency “v”.
Q.5. (c) Explain the Phenomenon of Beats. Obtain an expression or the beat frequency for the waves described by y? = A? cos 2? f?t and y? = A? cos 2? f?t.
Explain the Newton’s formula for the speed of the sound waves in air and discuss Laplace’s correction.