# Grade XI. Physics Exam Preparation Booklet. Chapter-wise Important Questions. #GrowWithGreen

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1 Grade XI Physics Exam Preparation Booklet Chapter-wise Important Questions #GrowWithGreen

2 Units and Measurements Q1. After reading the physics book, Anamika recalled and noted down the expression for the speed of efflux of a liquid of density ρ as However, he forgot to write ρ in the relation. Where should Anamika put the missing ρ? Q2. Three capacitors C 1, C 2 and C 3 are connected in series and its equivalent capacitance is C eq. If C eq = 0.15 ± 0.02 µf C 1 = 0.35 ± 0.07 µf and C 3 = 0.78 ± 0.13 µf Find capacitance of C 2 with error limits. Motion in a Straight Line Q1. The acceleration-time graph of a car is represented in the given figure. Write the time intervals for which the car has moved with (i) constant acceleration (ii) zero acceleration Q2. A body starts from rest with varying acceleration,. Obtain the change in position of the body. Q3. The minimum distance required by a truck, moving at a speed of 35 km/h, to stop is 40 m. Initially, if the truck was travelling at a speed of 70 km/h, then what would have been the minimum stopping distance? Q4. Derive the equations of motion for uniformly accelerated motion.

3 Motion in a Plane Q1. A particle undergoes uniform circular motion along a radius of 5 cm and with a speed given as v = 2 t t cm/s. Calculate: (a) the tangential acceleration at t = 2 seconds (b) the total acceleration at t = 2 seconds Q2. Find the value of α so that vector. is perpendicular to the vector Q3. A projectile is fired at an inclination so as to have maximum horizontal range. Show that the maximum horizontal range is four time the maximum height attained by the projectile. Q4. A man is walking with a speed 2m/s from east to west. Rain falls vertically with a speed of 10m/s. What is the direction in which he should hold his umbrella? Laws of Motion Q1. A block of mass 5 kg is placed on an adjustable inclined plane. The block just begins to slide down if the angle of inclination is made 60 with the ground. Calculate: (a) the coefficient of static friction (b) the force of static friction Q2. Three blocks of different masses, connected by light and inextensible strings, are pulled by a force F = 20 N as shown below. Calculate: 1. acceleration of each block. 2. tension in each string. Q3. Find the mass of the object in the following arrangement.

4 Q4. Newton s second law of motion is the basic law of motion. Explain (1 mark) Q5. A gun containing a bullet weighs M. The mass of each bullet is m. What will be the recoil velocity of the gun, if the bullet is fired will speed v? Q6. Calculate the value of the banking angle of a curved road of radius 350 m if it has a top speed of 20 m/s. (Ignore the effect of friction) Work, Energy and Power Q1. A particle is subjected to force F x that varies with position as shown in the figure. Find the work done by the force on the particle as it moves (a) from x = 0 m to x = 4 m (b) from x = 4 m to x = 8 m (c) from x = 8 m to x = 12 m (d) What is the total work done by the force over distance x = 0 m to x = 12 m. Q2. (i) Define conservative force. (ii) What is the equivalence of mass and energy? (iii) An electron is moving through a potential of 15 ev. What is the mass of the electron? Q3. State and prove the work energy theorem. Q4. A variable force, F acts on an object where: F = (3 x 2 2 x + 4) N How much work is done by this force in moving the object form x = 2 m to x = 4 m? Q5. Derive an expression for final velocities of two point objects colliding elastically with each other.

5 System of particles and Rotational motion Q1. Three identical thin rods, each of length L and mass M are welded perpendicular to each other as shown in the figure. The system is rotated about an axis passing through the end of one rod and is parallel to another. Find the moment of inertia of the system. Q2. A wheel starts with 3 rad/s and rotates with a constant angular acceleration 4 rad/s 2. Find (a) its angular displacement at t = 2s (b) its angular speed at t = 3s (c) number of revolutions in 2s Q3. Consider a seesaw of length l as shown in the figure. It has two blocks at the end points of masses m and M ( M > m ) respectively. At a moment, system rotates with an angular speed ω. Find an expression for the magnitude of the system s angular momentum. (Rod of seesaw is mass less). Q4. Two particles A and B of mass 3 kg and 5 kg respectively are projected from same ground level as show in the figure. Find the velocity of the centre of mass of the system.

6 Q5. Obtain an expression for the position vector of the centre of mass of a system of two particles of masses m 1 and m 2. r 1 and r 2 are the position vectors of the two masses. Q6. Prove that the radii of gyration of a hollow sphere and a solid sphere having the same radius ' r ' about an axis passing through their centers and perpendicular to their plane are in the ratio Gravitation Q1. The ratio of time periods of two satellites orbiting a planet is 2 : 3. Calculate the ratio of their orbital velocities. Q2. A planet made entirely of iron has a radius of m. What would be the value of acceleration due to gravity on its surface? [Density of iron = 7850 km/m 3 ] Q3. Show that the escape speed from the moon is about five times smaller than that from the earth. The radii of earth and moon are 6370 km and 1737 km respectively. Q4. Deduce the total energy expression of the satellite of mass m moving in a circular orbit around the Earth? Explain the significance of this energy being negative. Mechanical Properties of Solids Q1. Label the given stress-strain curve for a metal wire. (1 mark) Q2. How much pressure should be applied on a litre of water to compress it by 0.2%?

7 (Given that: Bulk modulus of water = N/m 2 ) Q3. State Hooke's law. What are the conditions in which this law is valid? Find the expression for young's modulus of material of a wire of length l, radius of cross-section r loaded with a body of mass M producing an extension l in it. Q4. Find the tensile stress and elongation in a metal wire of length 6 m and the diameter of cross- section is 28 mm on which a load of 20 kg is suspended. (Young's modulus of the metal = N/m 2, take g = 10 ms 2 ) Mechanical Properties of Fluids Q1. An insect walks on water surface with the help of its legs. Each leg has an approximately spherical shape of radius m. The mass of the insect is kg. Find the angle at which its six legs are supported on the surface of water. Assume the water temperature is 20 C. Surface tension of water is N/m. Q2. (i) Name the principle which helps us to determine the speed of efflux. (ii) A water tank has a small hole in its side at a height 25 cm from the bottom. The height of the water column in the tank is 1 m. The air pressure inside the tank above the water column is Pa. Calculate the velocity with which water will come out from the small hole. Q3. A hydraulic lift has two pistons of radii 10 cm and 25 cm each. How much force should one exert on the piston with a smaller radius in order to use the machine to lift a car of mass 2310 kg? Q4. Using the law of conservation of energy, derive Bernoulli s equation for steady fluid flow? (1+2 marks) Thermal Properties of Matter Q1. What is the relation between the coefficients of linear expansion, area expansion and volume expansion. What would be the change in volume of a glass rod, which is initially 75 cm long and 2 cm thick, if its temperature is increased by 50 C. [ glass = C 1 ] Q2. What do the flat portions in the given graph signify?

8 Q g of ice at 10 C is supplied with heat energy of 210 kj. What will be its final state and temperature? (Heat of fusion of ice = 333 kj/kg; specific heat capacity of ice = 2220 J/kg/k) Q4. The given figure shows a pine wall of thickness d p and a brick wall of thickness d b (= 3 d p ). The pine wall and brick wall sandwich two layers of unknown material having identical thicknesses and thermal conductivities. The thermal conductivity of pine is kp and that of brick is k b (= 15 k p ). After the steady state is reached, the following measurements of interface temperatures are obtained. T 1 = 25 C T 2 = 20 C T 5 = 10 C Find the value of T 4. Thermodynamics Q1. Calculate the total work done by a sample of an ideal gas if it is heated by applying an energy of 200 J. [Take γ = 1.5] Q2. (i) Establish the relation, (ii) Why is greater than? Q3. What is Carnot theorem? Describe Carnot cycle and derive an expression for efficiency of the Carnot engine. Q4. Derive the expressions for the work done in an adiabatic and isothermal process and show that the p-v curve of adiabatic process is always steeper than the isothermal process. Kinetic Theory Q1. Calculate the specific heat capacity of one gram mole of a solid containing number of atoms. Q2. Using, explain the rise in temperature on heating a gas with the help (2+1 marks)

9 of the kinetic theory of gases. Oscillations Q1. The cone of the loudspeaker of a music player vibrates in SHM at a frequency of 300 Hz where the amplitude of the cone is m and x = A at t = 0. (A) Find the velocity and acceleration as a function of time. (B) Find the velocity and acceleration at t = 2.4 ms Q2. A block of mass 2 kg is attached to the ceiling by two springs parallel to each other of same spring constant 30 N/m. Find the frequency of the vibration. Q3. A spring gets stretched by 0.16 m when a block of mass 0.4 kg is hanged on it. The spring block system is then placed on a horizontal frictionless table and the block is then pulled so that the spring is stretched by 0.2 m from the equilibrium point and then released. Find (A) spring constant (B) magnitude of maximum velocity (C) magnitude of maximum acceleration Q4. A block of mass 700 g is fastened to a spring whose spring constant is k = 56 N/m. The block is kept on a frictionless table and pulled to a displacement of x = 15 cm from its equilibrium position and released from rest at t = 0. (i) What is the amplitude of oscillation? (ii) What is the initial phase of motion? (iii) What is the displacement function x ( t ) for the spring-block system? Waves Q1. Two guitar strings having identical wavelengths of m are tuned to 450 Hz. The tension in one of the strings is increased by 2.5% when they are stuck. Find the beat frequency between the fundamentals of the two strings. Q2. A firehouse has a siren on the roof which makes sound of frequency of 802 Hz. The air near the siren is blowing with speed of 10 ms 1. (a) Find the wavelength of the sound travelling in the medium. (b) Fire-fighters are approaching near the siren at speed of 10 ms 1. What frequency do they hear? Speed of sound in still air = 343 ms 1. Q3. The function of a transverse pulse in a string at t = 0 is given by The pulse is travelling in the positive x -direction with a speed of 5ms 1. Write the function. (1 mark)

10 Q4. A travelling harmonic wave on a string is expressed as Calculate: (i) amplitude, frequency, and wavelength of the wave (ii) displacement and velocity of the wave at x = 2 cm and t = 1 s Q5. When a speeding car goes past a police radar van, it measures a drop of 14% in the pitch of the sound produced by the horn. The velocity of sound in air is 325 m/s. Calculate the speed of the car. Q6. Describe standing wave and normal modes in a stretched spring. Ray Optics Q1. (i) Show that a converging lens of focal length f, placed between an object and a screen fixed at a distance D, will form a real image on the screen for two lens (2+3 marks) positions separated by a distance d, given by. (ii) Show that the ratio of the image sizes at these two positions is. Q2. How does the material of a prism affect the deviation it produces in the path of light through it? Q3. (i) A ray of light is incident on a prism having an angle of 60. If it deviates by an angle of 30, then what limit can one put on the refractive index from this data? (1 mark) (2+1 marks) (ii) How will a red object look under a sodium lamp light? Q4. The power of a system of two convex lenses placed in contact is +2 D. If one of the lenses is replaced by a concave lens of same focal length, then the power of the system becomes +1.5 D. What is the focal length of the two convex lenses? Q5. What is the critical angle for a glass air surface, if a ray of light incident in air on the glass surface at an angle of 45 is deviated by 10? Q6. A combination of a flint glass prism and a crown glass prism ( μ v = 1.523, μ r = 1.515) produces dispersion of light without deviation. The

11 angle of prism of the crown glass prism is 6. What should be the angle of prism in the flint glass prism?

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