Chapter–2 Units and Measurements
Qn 1. Check whether the relation mv2 = mgh is dimensionally correct or not. Here v = speed, m = mass, g = acceleration and h = height
Qn 2. convert the unit:
6.67 × 10–11 N m2 (kg)–2 = ........... (cm)3 s–2 g–1.
Qn 3. Write the dimensional formula of these physical quantities:
electric potential V, resistance, pressure, power, density, universal constant of gravitation and potential energy.
Qn 4. Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using the method of dimensions.
Qn5. The centripetal force ‘F’ may depend upon the radius ‘r’ of the circle, mass ‘m’ and speed ‘v’ of the particle. Derive the expression for the Force F, using the method of dimensions.
Chapter 3: Motion in straight line
Qn1. What is a displacement vector?
Qn2. Define instantaneous velocity. Is the magnitude of instantaneous velocity different from the magnitude of instantaneous speed?
Qn3. The position of an object moving along x-axis is given by x = a + bt2
where a = 8 m, b = 2.5 m.s–2 and t is measured in seconds.- What is its acceleration at 2 s?
- What is the average velocity between t = 0.0 s and t = 2.0 s?
Qn4. Read each statement below carefully and state with reasons, if it is true or false :
- The total path length is always less than the magnitude of the displacement vector of a particle.
- the average speed of a particle is either less or equal to the magnitude of average velocity of the particle over the same interval of time,
Qn5 Draw these graphs (curves):
- v-t graph for uniformly accelerated motion
- x-t graph for uniformly accelerated motion
- v-t graph for uniform motion
- x-t graph for uniform motion
- x-t graph for stationary object
Qn6. An object is thrown vertically into the air. Draw a graph which represents the velocity (v) of the object as a function of the time (t)? The positive direction is taken to be upward.
Qn7. Derive equations of motion for uniform acceleration, using velocity-time graph.
Qn8. Define uniformly accelerated motion. Write a formula for instantaneous acceleration.
Qn9. An object falls freely. Plot these:
- (i) Variation of acceleration with time
- (ii) Variation of velocity with time
- (ii) Variation of position with time
Qn10. A ball is thrown vertically upwards with a velocity of 15 m/s from the top of a multi storey building. The height of the point from where the ball is thrown is 20.0 m from the ground. How long will it be before the ball hits the ground? Take g = 10 ms-2
Assertion and Reasoning
Directions: In the following questions, a statement of a assertion (A) is followed by a statement of reason (R ). Mark the correct choice as:
(A) if both assertion and reason are true and reason is the correct explanation of the assertion.
(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(C) If the assertion is true but the reason is false.
(D) If both assertion and reason are false.
(i) Assertion: A body can have acceleration even if its velocity is zero at that instant of time.
Reason: The body will be momentarily at rest when it reverses its direction of motion.
(ii) Assertion: When a body is dropped or thrown horizontally from the same height it would reach the ground at the same time.
Reason: Horizontal velocity has no effect on vertical motion.
(iii) Assertion: Displacement of a body may be zero when distance traveled by it is not zero.
Reason: The displacement is the longer distance between initial and final positions.
Chapter 4: Motion in a Plane
Qn1. Explain: unit vector, equal vectors.
- Write triangle law of vector addition.
- Write parallelogram law of vector addition.
Qn2. Two vectors are acting at an angle θ. Find expression for the magnitude and direction of their resultant.
Qn 3. Explain how do we subtract a vector A from another vector B
Qn 4. Define displacement vector. A particle is moving in the xy plane. Find vector expressions for its displacement, average velocity, instantaneous velocity and direction of velocity with respect to x axis. Use unit vectors i and j along the x and y axes respectively.
Qn 5. The position of a particle is given by r = 3.0t ˆi − t 2 ˆj + 4.0 kˆ meter
where t is in seconds and the coefficients have the proper units for r to be in meters.
- What is the magnitude and direction of velocity of the particle at t = 2.0 s ?
- find the acceleration ‘a’ of the particle?
Qn 6. 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?
- (B) What is the y-coordinate of the particle at that time?
- (C) What is the speed of the particle at the time ?
Qn7. A cyclist is riding at a speed of 18 km/h. As he approaches a circular turn on the road of radius 100 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second.
Qn 8 What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Qn 9. Find a mathematical expression for the path of a projectile which is thrown at an angle θ above horizontal. Also derive expressions for the time of flight T and range R.
Qn 10. Show that the projection angle θ for a projectile launched from the origin is given by θ = tan-1(4H/R)
Here the symbol H = maximum height attained by the projectile and R = the range of the projectile.
Qn 11. Explain with the help of vectors how a uniform circular motion is a kind of accelerated motion. Hence, find the expression for centripetal acceleration.
Qn 12. An insect trapped in a circular groove of radius 15 cm, moves along the groove steadily and completes 7 revolutions in 100 s.
- (a) What is the angular speed,
- (b) the linear speed of the motion and
- (c) acceleration?
Chapter 6: Laws of Motion
Qn1 A hammer of mass 1 kg moving with a speed of 6 m/s strikes a wall and comes to rest in 0.1 s. Calculate Impulse of the force Average retarding force that stops the hammer.
Qn 2. Case Based Question
Consider a box lying in the compartment of a train that is accelerating. If the box is stationary relative to the train, it is in fact accelerating along with the train. What forces cause the acceleration of the box? Clearly, the only conceivable force in the horizontal direction is the force of friction. If there were no friction, the floor of the train would slip by and the box would remain at its initial position due to inertia (and hit the back side of the train). Answer these questions:
(i) the friction that provides the same acceleration to the box as that of the train, keeping it stationary relative to the train is
(a) Static (b) dynamic (c) kinetic (d) sliding
(ii) Limiting friction is the maximum value of …………… friction
(a) Static (b) dynamic (c) kinetic (d) sliding
(iii) The maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and the train’s floor is 0.15 and g = 10 ms-2 is
(a) 1 ms-2 (b) 0.5 ms-2 (c) 1.5 ms-2 (d) 0.15 ms-2
(iv) which friction is minimum?
(a) Static (b) dynamic (c) kinetic (d) rolling
Chapter 7: Work Energy and Power
Qn 1. A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
- (a) work done by the applied force in 10s,
- (b) work done by friction in 10 s,
- (c) change in kinetic energy of the body in 10 s,
Qn 2. Find the work done by a force F = (3 i + 4 j + 5 k) unit which makes displacement
d = (5 i - 4 j + 3 k) unit in 2 s. Calculate average power. Here i, j and k are the unit vectors along the axes.
Chapter 8: Gravitation
Ch 9 MECHANICAL PROPERTIES OF SOLIDS
1.Steel is more elastic than rubber. Explain.
2. State and explain Hooke’s law. A wire is fixed at one end and is subjected to increasing load at the other end. Draw a curve between stress and strain.With the help of the curve, explain the term elastic limit, yield point, breaking point and permanent set. How can this curve be used to distinguish between ductile and brittle substances?
3. Define stress and strain.
4. Define Poisson's ratio.
5. Define elastic energy. Find its expression in terms of stress and strain.
Chapter 10: MECHANICAL PROPERTIES OF FLUIDS
1. Write Pascal Law. Explain any one applications of Pascal’s Law.
2. Explain the effect of Temperature on viscosity of (a) Liquid (b) Gases.
3. State and prove equation of continuity.
4. State and prove Bernoulli’s theorem. Explain any two applications of Bernoulli’s theorem.
5. Explain capillary phenomenon and derive an expression for height of fluid in a capillary tube raised due to capillary action (Ascent formula)
6. Derive the expression for terminal velocity of a sphere, falling in a vessel filled with fluid.
7. Derive the expression for excess pressure in a liquid drop.
8. Define surface tension. Write it's SI unit.
9. State stoke's law. Name a force which is proportional to the velocity.
10. Define coefficient of viscosity. Write it's SI unit.
11. Explain lift on airfoil.
12. Explain principle of atomizer.
13. Define hydraulic pressure. Prove that the liquid liquid pressure depends on its density and depth
Chapter–11: THERMAL PROPERTIES OF MATTER
1. State Wien’s displacement law. A hot body has a surface temperature of 1327°C. Determine the wavelength at which it radiates maximum energy. Given Wien's constant = 2.9 x 10-3 mK.
2. State Stefan-Boltzmann law.
3. Draw a graph representing black body radiations.
4. Establish the relationship among the coefficients of thermal expansions: α and γ.
5. Explain why heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.
6. Define these: thermal conductivity, specific heat capacity, latent heat of fusion
7. Write the different modes of transfer of heat. Give one example of each.
8. Draw a curve of temperature versus time when an ice cube is heated and changes phase.
9. What is the anomalous expansion of water? What is its advantage for animals living in a freezing lake?
10. At what temperature the density of water is maximum. Draw a curve between the density and temperature for a freezing water.
Chapter–12: THERMODYNAMICS
1. State first law of thermodynamics. Using it, derive the relationship between Cp and Cv. What are the limitations of the first law of thermodynamics?
2. Define an adiabatic process. Derive an expression for work done during an adiabatic process. What are the essential conditions for an adiabatic process to occur?
3. What is an isothermal process? Derive an expression for the work done during an isothermal process.
4. What are the two essential conditions for an isothermal process to take place?
5. What is internal energy?
6. What happen to the internal energy of a gas during
- (i) isothermal expansion
- (ii) adiabatic Expansion.
7. Why is the molar specific heat capacity at constant pressure greater than the molar specific heat capacity at constant volume?
8. Define Reversible process and give an example.
9. Define an irreversible process and write an example.
10. State zeroth law of thermodynamics.
11. State second law of thermodynamics.
12. What are thermodynamic state variables?
13. Distinguish between extensive and intensive state variables, give examples of each type.
14. On removing the valve of a bicycle tube, the air escaping from the bicycle tube cools why?
15. What are isobaric and isochoric processes?
16. What do you mean by quasi-static process?
17. Prove that Cp - Cv= R known as Mayer's relation.
Chapter–13: KINETIC THEORY OF GASES
1. What is the ratio of rms speed of oxygen and hydrogen molecules at a particular temperature?
2. Derive an expression for pressure exerted by an ideal gas using kinetic theory of gases. What is kinetic interpretation of temperature?
3. What does " free path" mean for gas molecules? Write an expression for it.
4. State law of equipartition of Energy. Using this law, find the value of Cp, Cv and γ for rigid diatomic gas.
5. Define degrees of freedom of a gas.
6. Find the degree of freedom for:
(a) monoatomic gas (b) diatomic gas
7. What will be the change in the ratio P/ρ as temperature is maintained constant.(here P= pressure and ρ= density of gas)
8. Oxygen and hydrogen are at the same temperature. What is the ratio of kinetic energies of their molecules when oxygen is 16 times heavier than hydrogen?
Chapter 14: OSCILLATIONS
1.Define simple harmonic motion. Prove that the oscillation of a simple pendulum is SHM. Hence derive an expression for its time period.
2. Deduce an expression for the velocity of a particle executing S.H.M. When is the particle velocity (i) Maximum (ii) minimum?
3. Draw these graphs of a particle executing SHM (phase angle equal to zero)
(i) displacement time (ii) velocity time graph and (iii) acceleration time graph.
4. (a) A spring of force constant k is attached with a mass m and is made to oscillate. Derive expression for its time period.
(b) If the spring is divided into three equal parts. What would be the force constant for each individual part?
5. Find expression for energy of a simple harmonic oscillator.Draw curves for PE and KE.
6. A spring having with a spring constant 1200 Nm-1 is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine
- (i) the amplitude and frequency of oscillations,
- (ii) maximum acceleration of the mass, and
- (iii) the maximum speed of the mass.
Chapter 15: WAVES
1. Write displacement relationship for a progressive wave.
2. What are stationary waves? Derive it's displacement relationship.
3. Prove that only odd harmonics are formed in organ pipes closed at one end, or frequency of harmonics is in the ratio 1:3:5
4. Show that all harmonics are present in the oscillation in the open pipe.
5. List out the differences between a progressive wave and a stationary wave.
6. In which medium do the sound waves travel faster: solids, liquids or gasses?
7. What is the effect of pressure on speed of sound in air provided temperature remains constant ?
8. The ratio of amplitude of two waves is 2:3. What is the ratio of intensities of these waves?
9. What is the distance between a node and an adjoining antinode in a stationary wave?
10. If the tension of a wire is increased to four times, how is the wave speed changed?
11. Two sources of sound produce 20 beats in 4 seconds. What is the difference in frequencies of the two sources?
12. What are beats? Show that the number of beats produced per second is equal to the difference in frequencies.
13. A transverse harmonic wave on a string is described by
y(x, t) = 3.0 sin (36πt + 0.018 x + π/4)
where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave ?
If it is travelling, what are the speed and direction of its propagation ?
(b) What are its amplitude and frequency ?
(c) What is the initial phase at the origin ?
(d) What is the least distance between two successive crests in the wave ?
14. For the travelling harmonic wave
y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35)
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
(a) 4 m, (b) 3λ/4
15. Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?
16. The transverse displacement of a string (clamped at its both ends) is given by
y(x, t) = 0.06 sin (2π/3).x.cos (120 πt)
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 ×10- 2kg.
Answer the following :
(a) Does the function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave ?
(c) Determine the tension in the string.
17. Use the formula v = (γP/ρ)1/2
to explain why the speed of sound in air
(a) is independent of pressure,
(b) increases with temperature,
(c) increases with humidity.
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