Physics Question Paper

Cheatsheet Content

### 1. UNITS & MEASUREMENTS 1. Which one of the following fundamental forces in nature binds protons and neutrons together in a nucleus? a) Gravitational force b) Electro-magnetic force c) Strong nuclear force d) Weak nuclear force 2. Select the strongest force from the following list. (Electromagnetic force, Gravitational force, Weak nuclear force) 3. Choose the correct answer from the brackets: Weakest force in nature is.... (Strong nuclear force, Electromagnetic force, Gravitational force, Weak nuclear force) 4. The correctness of an equation can be checked using the principle of homogeneity in dimensions. a) State the principle of homogeneity. b) Using this principle, check whether the equation $x = ut + \frac{1}{2}at^2$ is dimensionally correct 5. A The centripetal force on a body of mass 'm' and velocity 'v' moving in circular orbit of radius 'r' is given by $\frac{mv^2}{r}$. a) Write the dimensional formula of force. b) Derive $F_c = \frac{mv^2}{r}$ by using dimensional analysis 6. The correctness of equation can be checked using the principle of homogeneity in dimensions. a) State the principle of homogeneity. b) Using this principle, check whether the equation $f = \frac{1}{2\pi}\sqrt{\frac{g}{l}}$ is dimensionally correct, g Where f-frequency, l-length and g-acceleration due to gravity. c) The velocity V of a particle depends on time 't' as $V = At^2 + Bt$. Find the dimensions and units of A & B 7. What is the area of the square of side 1.4 cm in proper significant figures? 8. All physical quantities can be expressed in terms of dimension. a) Write the physical quantities of the following dimensions: i) $[M^1 L^1 T^{-1}]$ ii) $[M^1 L^2 T^{-2}]$ b) Check whether the equation $T = 2\pi\sqrt{\frac{m}{g}}$ Where T is the time period of a simple pendulum c) m → mass of g the bob, g → acceleration due to gravity. 9. a) A student writes the equations for the relativistic variation of mass with velocity as $m = \frac{m_0}{\sqrt{1-\frac{x}{c^2}}}$ Where '$m_0$' is the rest mass and 'c' is the speed of light. What is the dimensional formula for 'x'? b) State the no of significant figures of the following i) 1.37 ii) 10.05 iii) .007m² iv) .050 N v) $3.6 \times 10^6$ vi) $2.02 \times 10^{-2}$ 10. Round the following figures to 3 significant figures a) 2.746 b) 2.745 c) 2.743 ### 2. MOTION IN A STRAIGHT LINE 1. (a) Define uniform motion. (b) Draw the velocity - time graph of a uniformly accelerated motion. (c) Using the graph obtain the equation $x = vt + \frac{1}{2}at^2$ 2. From V - t graph derive the expression $v^2 = u^2 + 2as$ 3. a) Slope of V-t graphs gives....................... b) From v-t graph derive the expression $v = u + at$ 4. The velocity - time graph of an object is given below. a) The area under this graph gives...... b) Derive the relation $s = ut + \frac{1}{2}at^2$ using above graph 5. a) Calculate displacement b) Calculate distance | V | 11 | 16 | 21 | 26 | 31 | 36 | |---|----|----|----|----|----|----| | T | 0 | 1 | 2 | 3 | 4 | 5 | 6. a) Draw v- t graph & a – t graph b) Find the distance travelled by the car in 6 sec 7. Acceleration is the time rate of change of velocity. Give an example of a body possessing zero velocity and still accelerating. 8. a car of mass 1000 kg starts from rest at t = 0 & under goes acceleration as shown in figure. a) Draw corresponding v-t graph b) What is the retarding force acting on the car? c) What is the total distance from t = 0 to t = 4 sec ### 3. MOTION IN A PLANE 1. An object is projected with an initial velocity $v_0$ making an angle $\theta$ with the horizontal. (a) What is the shape of the path of the projectile? (b) Obtain an equation for time of flight and horizontal range of the projectile. (c) Obtain expression for height of projectile 2. The position vector r of a particle P located in an x-y plane is shown in figure. (a) Redraw the figure by showing the rectangular components. (b) Write the position vector in terms of rectangular components. 3. If A is perpendicular to B. What is the value of A•B? a. Find the angle between the force $\vec{F} = (3\hat{i}+4\hat{j}-5\hat{k})$ N and displacement $\vec{d} = (5\hat{i}+4\hat{j}+3\hat{k})$ m. 4. a) Identify the scalar quantity from the following alternatives. (i) Momentum (ii) Work (iii) Torque 5. A stone is thrown with the help of a sling with initial velocity $v_0$ at an angle '$\theta$' from the horizontal. a) Working of sling is based on............Law of vector addition. b) With the help of a vector diagram, state this law. 6. a) Find whether the given vectors $(2\hat{i}+3\hat{j}+4\hat{k})$ and $(4\hat{i}+6\hat{j}+8\hat{k})$ are parallel or not. b) What are orthogonal unit vectors? 7. A parallelogram law helps to find the magnitude and direction of the resultant of 2 forces: a) Derive equation resultant of parallelogram law of vector addition b) State the law. c) If the magnitude of two vectors and their resultant are the same, what is the angle between the two vectors? ### 4. LAWS OF MOTION 1. Using Newton's second law of motion, derive the equation $F=ma$ 2. A vehicle of mass m is moving on a banked road of radius r. (a) What are various forces acting on the vehicle? (b) Obtain an expression for maximum safe speed of the vehicle on a banked road. 3. A person drives a car along a circular track on a level ground. (a) Derive an expression for the maximum safe speed of the car. (b) Why do we give banking to curve roads? 4. We are familiar with Newton's laws of motion. (a) State Newton's second law of motion. (b) Using the above law, explain i. Impulse – momentum principle ii. Law of conservation of linear momentum (c) A circular racetrack of radius 300 m is banked at an angle of 15º the coefficient of friction between the wheels of a race car and the road is 0.2. Find: i. The optimum speed of the race car to avoid wear and tear on its tyres. ii. Maximum permissible speed to avoid slipping. 5. When a short is fired from a gun, the gun is moved in the backward direction. a) State the principle behind it. b) Prove the principle using Newton's second law of motion. c) The recoil velocity of the gun is an example of this principle. 6. If a child of mass 20 kg is sitting inside a lift in a multi- storied building. a) What will happen to the weight of the child if? i. The lift moves up with a constant speed? ii. The lift moves up with a constant acceleration? b) Write down expressions for the apparent weight felt by the child when the lift is: i. Ascending. ii. Descending with a uniform acceleration. c) If the child weighs 20kg and if the lift is moving down with a uniform acceleration of $5ms^{-2}$, what will be the apparent weight of the child? (g = $10ms^{-2}$). 7. A shell of mass 0.5kg moves with a muscle speed of 20m/s. If mass of gun 10kg, find recoil velocity ### 5. WORK ENERGY AND POWER 1. An object is dropped from a height H as shown below: a) Show that total energy is conserved at the points A, B and C. b) Show variation of KE & PE. During Free fall 2. Two bodies of masses m1 and m2 have the same linear momentum. What is the ratio of their kinetic energies? 3. A body is pushed with a force of 3N for 2S along a frictionless track. How much work is done by the force? 4. A car and a truck have the same kinetic energies at a certain instant while they are moving along two parallel roads a) Which one will have greater momentum? b) If the mass of truck is 100 times greater than that of the car, find the ratio of velocity of the truck to that of the car. 5. a) State the work energy theorem. b) Show that the potential energy of a body is completely converted into kinetic energy during its free fall under the gravity. 6. a) State and explain the work done in the following situations: i) A person carrying a heavy load walks on a level road. ii) A man spending his energy by pushing on a concrete wall. b) A constant force of 200 N displaces a body through 5m in the direction of the force. Find the work done on the body 7. Derive an equation for potential energy of a spring & draw its graph 8. Write three examples for +ve, -ve & zero work ### 6. ROTATIONAL MOTION 1. (a) Show that $\tau = \frac{dL}{dt}$, for rotational motion. (b) State the law of conservation of angular momentum. 2. Derive the expression for kinetic energy in rotational motion. 3. The rotational analogue of mass is called............. 4. A solid cylinder of mass 20 kg rotates about its axis with $\omega = 100 rad/s$. if radius is 0.25 m. what is angular momentum 5. A girl rotates on a swivel chair as shown below. a. What happens to her angular speed when she stretches her arms? b. Name and state the conservation law applied for your justification. 6. a wheel starting from rest acquires an angular velocity of 10 rad /s in 2 seconds. The moment of inertia of the wheel is .4kgm². Calculate for acting on it 7. Write a short note about principle of moment ### 7. GRAVITATION 1. State Kepler's Law of orbits and Law of periods. 2. Derive an expression for the variation of g with height (h) above the surface of the earth. 3. Earth satellites are objects which revolve around the earth. a) Time period of a geostationary satellite is........... b) Derive an expression for the time period of a satellite. 4. Derive an expression for escape speed from a planet. 5. Find the height at which g is reduced to g/2 6. Acceleration due to gravity decreases with depth. a) Prove the above statement by deriving the proper equation. b) Using the equation, show that acceleration due to gravity is maximum at the surface and zero at the center of the earth. 7. The value of acceleration due to gravity (g) is same for all objects at a given place. Derive an equation for the acceleration due to gravity in terms of radius (R) and mass (M) of the earth. Arrive at mathematical expressions for variation of g below and above the surface of the earth. 8. The velocity of a satellite in its orbit is called orbital velocity. a) Find the relation between orbital velocity and escape velocity. b) Moon has no atmosphere. Why? ### 8. SOLIDS 1. A steel wire has a radius of 10 mm and a length of 1 m. A 100 kN force stretches it along its length. Calculate the stress and elongation on the wire. Young's modulus of steel is $2 \times 10^{11} Nm^{-2}$ 2. The stress-strain graph of two materials A and B are shown below. (a) State the law which relates stress with strain. (b) Which of the two materials has the greater Young's modulus? (c) Which of the two materials is more ductile? 3. a) The ratio of shear stress to shear strain is ............. (i) Poisson's ratio (ii) Young's modulus (iii) Bulk modulus (iv) Rigidity modulus b) State Hooke's law. 4. When a mass is suspended on a metallic wire, the length of the wire increases slightly. a) Draw the stress – strain graph of a loading wire. Mark the following points: i. Elastic limit ii. Fracture point iii. Plastic region iv. Elastic region b) If the young's module of iron and glass are $190 \times 10^9 Nm^{-2}$ and $65 \times 10^9 Nm^{-2}$ respectively. Which is more elastic? Justify your answer. 5. Modulus of elasticity of a material is the ratio of stress and strain. a) Young's modulus for a perfectly rigid body is ----------- b) One end of a rope of a length 4.5 m and diameter 6 mm is fixed to the branch of a tree. A monkey weighing 100N jumps to catch the free end and stays there. Find the elongation of the rope. (Young's modulus = $4.8 \times 10^{11} N/m^2$). 6. Derive an expression for potential energy of string & energy density ### 9. FLUIDS 1. A car having mass 1350 kg is placed in a hydraulic lift. If the radius of the small piston is 5 cm and the radius of the large piston is 15 cm, calculate the amount of force to be exerted on the small piston to lift the car. (g = $9.8 m/s^2$) 2. Derive an expression for capillary rise of a liquid in a capillary tube. 3. Define Terminal velocity. Write the equation for terminal velocity. 4. Consider a fluid moving in a pipe of varying cross-sectional area as shown in figure. $a_1$, $a_2$ are cross sectional areas of pipe and $v_1$, $v_2$ are the velocities of fluid. (a) State Bernoulli's principle. (b) Derive Bernoulli's equation. (c) Write the equation of stoke's law. 5. State Pascal's law for transmission of fluid pressure and explain the principles of working of a hydraulic lift. 6. A liquid surface behaves like a stretched elastic membrane. a) Name the liquid property for the above behavior. b) Define angle of contact. What is its value for pure water with glass? 7. Rain drops are being accelerated while falling through the atmosphere. But they reach at the surface of the earth with a uniform velocity. a) What is this velocity called? b) Obtain an expression for the excess pressure inside a rain drop. 8. Explain Toricellis law ### 10. THERMAL PROPERTIES OF MATTER 1. Temperature is the degree of hotness of a body. (a) Temperature of a normal human body is 98.6 °F. What is the corresponding temperature in the Celsius scale (b) Define latent heat? 2. A body cools from 80° C to 50° C in 5 minutes. Calculate the time it taken to cool from 60° C to 30°C. The temperature of the surrounding is 20° C. 3. Linear expansion is a change in length of an object with temperature. a. Write the equation for the coefficient of linear expansion. b. Show that the coefficient of volume expansion is thrice its coefficient of linear expansion. c. The absolute zero is...........[-273.15°C, 273.15K, 273.15°F, 0°C] 4. a) Explain Anomalous behavior of water b) Draw graph of change of state. 5. Differentiable between sea Breeze & land Breeze 6. State Stefan's boltsman law ### 11. THERMODYNAMICS 1. The P-V diagram of a Carnot engine is given below: (a) Which are the four thermodynamically processes represented in the above P-V diagram? b) Write an equation to calculate the efficiency of a Carnot engine. 2. (a) Derive an expression for work done in an isothermal process. (b) What is the work done in an isochoric process? 3. a) derive an equation to calculate efficiency of a cannot engine b) A Carnot engine is working between in melting point & steam point. What is its efficiency? 4. Derive the relation $C_p - C_v = R$ where $C_p$ and $C_v$ are molar specific heat capacities of an ideal gas at constant pressure and volume respectively and R is the universal gas constant. 5 A thermodynamic process is one in which the thermodynamic variables (P, V, T etc.) change. a) Name the thermodynamic process in which $PV^\gamma = constant$. b) State and explain first law of thermodynamics. c) Derive an expression for the work done in an adiabatic process involving an ideal gas in terms of pressure and volume. 6. a) Which thermodynamics process is also called an isentropic process? b) Find efficiency of a Carnot engine works between ICE point & Steam point 7. State zeroth & first law in thermodynamics ### 12. KINETIC ENERGY OF GASES 1. Derive an expression for the pressure exerted by an ideal gas based on kinetic theory. 2. What do you mean by Mean free path? Give an equation for Mean free path. 3. By using the law of equipartition of energy, derive the value of ratio of specific heats of a mono atomic gas 4. According to the kinetic theory of gases, gas molecules are always in random motion. a. State the law of equipartition of energy. 5. Kinetic theory of gases is based on the molecular picture of matter. a) Write any five postulates of kinetic theory of gases. b) Write short note on: i) Equipartition of energy ii) degree of freedom ### 13. OSCILLATION 1. Derive an expression for period of oscillation of a loaded spring 2. A simple pendulum in oscillatory motion is shown in figure. a) Mark the different forces acting on the bob. b) Derive an expression for the time period of the simple pendulum. 3. What is the time period of a second's pendulum? 4. a) Define Simple Harmonic motion (SHM). b) For a SHM, time period T=2s. If displacement from the mean position is 10 cm, calculate the instantaneous acceleration. c) Graphically show the variation of Kinetic energy of a simple pendulum is SHM with its position. 5. Represent Simple Harmonic Motion graphically. a) A spring with spring constant 1200 N/m is mounted on a horizontal table as shown. 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 cm and released. ### 14. WAVES Determine: i) Frequency of Oscillations. ii) Maximum acceleration of the mass. 6. Find the position where KE is equal to PE 1. A wire 0.72 m long has a mass of $5 \times 10^{-3}$ kg. If the wire is under a tension of 60 N, what is the speed of transverse waves on the wire? 2. A transverse harmonic wave on a string is described by $y(x,t) = 3.0 \sin (36t + 0.018x + \pi/4)$ where x and y are in cm and t in s. (a) Is this a travelling wave or a stationary wave? (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? 3. In resonance column experiment, we can hear maximum sound at a certain height. This is due to the Phenomenon of resonance. a) Show that for a pipe closed at one end, the frequencies are in the ratio $v_1 : v_2 : v_3 = 1 : 3 : 5$. b) Open pipes are preferred to closed pipes in musical instruments. Why? c) Show for an open pipe the frequencies are in the ratio 1:2:3 4. Write newtons equation and newtons laplace equation.