FOR HALF YEARLY EXAM (XI) Mob: 9861210706, 9777702608 E-mail: basant.physics@gmail.com BASANT S PHYSICS 1. Two masses m1 and m2 are in contact. If a force F acts on m 1 or m 2, what is the ratio of the acceleration? 2. A ball of mass 5kg strikes against a wall at an angle of 45 0 and is reflected at the same angle. Find the change in momentum. 3. The material with which two planets are made is same, what is the dependence of g on the radius? 4. A river is flowing from west to east at a speed of 5m/min. In what direction should a man on the south bank swimming at 10m/min in still water, should swim to cross the river along the shortest path? Also find the time taken (width of river- 1000m). 5. With relevant vectorial diagram, prove that the magnitude of the centripetal acceleration is v 2 /r for a body moving with constant speed in a circular path of radius r. 6. Prove that the apparent weight of a person increases or decreases in a lift (accelerated). 7. A spring of half a metre length is used to whirl a 1kg stone in a vertical circle at uniform speed of 5m/sec. What is the maximum tension in the string? Also find the tension minim 8. What is the work done in stretching a wire by the application of force? (Given its length, area, force and young s modulus are l, A, F and Y respectively). 9. The length and breadth of a rectangular lamina are recorded as, l = (15.12 0.01) cm and b= (10.15 0.01) cm respectively. What is the percentage error in its area? 10.A ball falls freely from rest on a perfectly elastic surface from a height of 3m. Draw the v- t graph for it up to 5 seconds. 11.(i) Path of a projectile is a parabola- Establish. (ii) Find the time of flight for it. 12.(i) Define escape and orbital velocity (ii) Derive relations for both for near to earth orbits and relate them. 13.A carpet is wound round to form a cylinder of radius R. If it gets unwound, find (i) Moment of inertia after the radius becomes R/2 (ii) Velocity of its center of mass when radius R/2.(Given the mass of the carpet is M) 14.(i) What is the condition under which the equations of motion can be used? (ii) Derive v 2 = u 2 + 2as. (iii) Write two significance of v t graph. (i) (ii) (iii) (iv) What is limiting friction? Is friction a self adjusting force? What are the factors affecting the force of friction? Find the coefficient of friction required to hold a mass M at rest on a vertical wall by applying a force F on it. 15.If the radius of a sphere has a % error of 2, what is the percentage error in its volume? 16.What is the condition to be satisfied for a mass tied to a string to perform a vertical circle? 17.Find the ratio of acceleration due to gravity on the surface of two planets, made of the same material. 18. A body drops a stone into a well. It takes 4.2 seconds for the sound of splash to reach him. If the depth of water level is 78.4 meters find the velocity of sound I the medium? 19.Derive the safe velocity of a cyclist negotiating a curve. 20.Define the angle of friction and angle of repose. How are they related? 21.Is uniform circular motion, a constant accelerated motion? Give reason for your answer. 22.Rain is falling vertically with a velocity v. In what direction should a man moving with a velocity v m hold his umbrella, so that he does not get drenched?
23.A rod of length l is fixed between two rigid walls. If Y and a are its Youngs modulus and linear expansion coefficient respectively, what will be the thermal stress on the walls if uniformly heated? 24.(i) State parallel- axis theorem. (ii) What is the moment of inertia about an axis passing through the edge as a tangent in the plane of a disc of mass M and radius r? 25.The percentage error in the measurement of the quantities a, b and c are 1%, 2% and 3% respectively. Find the percentage error in the measurement of p if p = a 2 b 3 / c. 26.A cycle accelerates from rest at a constant rate 2m/s 2 for some time and then decelerates to come to rest at a constant rate 1 m/s 2. If the total time elapsed is 6 seconds, find (i) maximum velocity attained. (ii) The total distance traveled. 27.State Keppler s laws of planetary motion. 28.(i) What are dimensions? (ii) What does the law of Homogeneity says? (iii) Give three applications of dimensions. (v) If energy E, length l and time T are fundamental, what is the dimension of mass? 29.(i) Distinguish between elastic and inelastic collision. (ii) Deduce a relation for the velocity of the masses after collision, if their velocities in a straight line before collision is u 1 and u 2. (i) (ii) (iii) Explain how law of conservation of energy is obeyed in a vibrating spring. Show the energy vibration with position. Derive an expression for velocity at any position between the mean position and the extreme. 30.(i) Derive a relation for terminal velocity of a sphere of material density allowed to come down a liquid of density and coefficient of viscosity. (ii) If eight drops of radius r, coalesce, what will be the effect on their terminal velocity? With a neat diagram, explain how Carnot explained the function of a cyclic- reversible process. 31.What is the principle underlying the function of a rocket? Develop a relation for its velocity at any instant of motion. Also find the thrust associated. What is capillary rise? Derive a relation for the height raised by a liquid in terms of surface tension. What will happen if a tube of insufficient length is dipped in the liquid? 32.Why there is no atmosphere on the moon? 33.Give an example each for a body where the center of mass lies inside the body and outside the body. 34.A force F = I + 5j + 7k acts on a particle and displaces it through S = 6i + 9k. Calculate the work done if the force is in Newton and displacement in metre. If a force of 2i + 5j displaces a body from (2, 1, 1) to (1, 2, 3) find the work done. 35.A stone is dropped from the top of a cliff. If it reaches the ground in 4s, calculate height of the cliff. (g = 9.8ms -2 ) 36.A body is strained within elastic limits. Show that work done, in the process is ½ x stress x strain. 37.Derive the equation of motion graphically x(t) = x(0) + v(0)t + ½ at 2. 38.Compare the kinetic energy and potential energy of a simple harmonic oscillator when its displacement from mean position is half of its amplitude. 39.State theorems of parallel and perpendicular axes of moment of Inertia for a plane lamina 40.Distinguish between conservative and non- conservative force with an example each. 41.Find the angle between A = i +2j k and B = i +j 2k. 42.Prove that during head on elastic collision particles of identical masses exchange their velocities. 43.State the law of static friction. What is angle of friction?
44.Define escape velocity. Derive an expression for escape velocity of an object from the surface of a planet. 45.A X- ray photon of 14KeV energy is emitted by a nucleus of mass 235 m. u. what is the momentum of the recoiling nucleus? 46.Convert 1 Joule into ergs (C.G.S. units) using dimensional analysis. 47.A body is moving along a circular path with constant speed. Derive an expression for centripetal force acting on the body. 48.What is a projectile? Derive an expression for range of the projectile and hence prove that range is maximum when body is projected at an angle of 450 from the horizontal. A fighter plane flying horizontally at an altitude of 1.5km with speed 720km/hr. passes directly overhead an anti- aircraft gun. At what angle from vertical should the gun be fired for the sheel with muzzle speed 600ms -1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10ms -1 ) Rain is falling vertically with a speed of 30ms -1. A woman rides a bicycle with a speed of 10 ms-1 in the north-south direction. What is the direction in which she should hold her umbrella? 49.A man weighing 60kg stands on a spring weighing machine inside a lift. Obtain the reading on the machine when Lift ascends upwards with a uniform velocity of 10 ms -1 Lift ascends upwards with a uniform acceleration of 2 ms -2 c. Lift descends downwards with a uniform acceleration of 2 ms -2 d. Falls freely (g = 10 ms -2 ) Consider a mass m attached to a string of length l performing vertical circle. Find an expression for (i) velocity at any point, (ii) Tension at any point (iii) Velocity minimum at the lower most point for performing a vertical circle. 50.Give an example when a body has zero velocity and still has acceleration. 51.Name two factors which determine whether a planet has an atmosphere or not. 52.How does soap help us to remove dirt better in washing clothes? 53.Velocity of a projectile is 10m/s. At what angle of the horizontal should it be projected so that it covers maximum horizontal distance? 54.Justify the statement that a uniform circular motion is an accelerated motion. 55.Distinguish between conservative and non-conservation forces with one example each. 56.Find the work done in moving a particle along a vector S = 4i j + 7k if the applied force is F = i + 2j - k Newton. S is in metre. 57.Why does a cyclist lean inward negotiating a curve? Explain with diagram. 58.Kinetic energy of a particle is increased be 300%. Find the percentage increase in momentum. 59.A man moving in rain holds his umbrella inclined to the vertical even though the rain drops are falling vertically down wards. Why? 60.A cricket ball of mass 150grams moving with a peed of 12ms -1 is hit by a bat so that the ball is turned back with a velocity of 12ms -1. Calculate the impulse received by the ball. 61.Establish the relation between torque and angular acceleration. Hence define moment of inerti Establish the following relations: i. ii. L = I iii. =I 62.The string of a pendulum is 2.0m long. The body is pulled sideways so that the string becomes horizontal and then the bob is released. What is the speed with which the
bob is released? What is the speed with which the bob arrives at the lowest point? Assume that 10% of the initial energy is used against air resistance g = 10m/s 2. 63.Define escape velocity. Derive an expression for escape velocity of an object from the surface of a planet. 64.Name three types of basic forces in nature and briefly discuss their characteristics. 65.Derive an expression for the distance travelled by a uniformly accelerated body in t seconds. Also derive an expression for the distance travelled by the body in the nth second. 66.The dimensional formula of impulse is MLT -1. Name another physical quantity having the same dimensions. 67.The magnitudes of vectors A, B and C are 5, 12 and 13 units respectively and A + B = C. What is the angle between vectors A and B? 68.Two bodies A and B weighing 5kg and 6kg respectively have equal momentums. Which one has more kinetic energy? 69.Two identical solid discuses are released from the top of an inclined plane. One slips down without rolling while other rolls down without slipping. Which one will reach the bottom first? 70.Derive the relation v 2 = u 2 + 2as for constant acceleration. Derive the expression s = ut + ½ at 2 for a body moving with uniform acceleration. 71.State the law of conservation of angular momentum. Explain with an example. 72.How much work a man will do in carrying a 10kg load over his head horizontally on smooth surface for 10 metres? 73.State two advantages of friction in daily life. By what factor the velocity of a body should be increased so that its kinetic energy is increased by factor of nine? Justify your answer. 74.A bullet of mass 100g moving with 20m/s strikes a wooden planck and penetrates upto 20cm. calculate the resistance offered by the wooden planck. 75.A cyclist leanes towards the centre while negotiating a curved path. Why? If the earth suddenly shrinkes wihtout any change in mass, what will be the duration of the day. 76.A ring of mass 10kg and diameter 0.2m is rotated about its axis. It makes 1800 revolutions per minute. Find (a) moment of inertia (b) angular momentum and (c) rotational energy by ring. 77.Derive an expression for moment of intertia in a circular disc about its axis passing through the centre and perpendicular to its plane. 78. (a) Define orbital velocity and establish an expression for it. (b) Calculate the value of orbital velocity for an artificial satellite of earth orbiting at a height of 100km. (Given: Mass of earth = 6 x 1024kg, Radius of earth = 6400km) i. How g varies with depth? Derive the relation. ii. What is the effect of rotation on the value of g? Derive the relation. 79.A body is projected with 20m/s at an angle of 600 from horizontal direction. Calculate: i. the total time of flight. ii. the maximum height attained. iii. the horizontal range. iv. The angle of projection at which the horizontal range will be maximum. Distinguish between a uniform and non-uniform circular motion. For a uniform circular motion find the centripetal acceleration? If the speed is variable in circular path, give the net accelertion. 80.State the Newton s second law of motion. 81.What is analogous to mass in rotational motion?
82.Name the two factors which determine atmosphere on the surface of a plant. 83.A car moving along a straight highway with a speed of 72kmh -1 is brought to a stop within distance of 100m. What is retardation of car and how long does it take for the car to stop? 84.Prove that friction is a necessary evil. 85.A particle of mass m revolves in a horizontal circle of radius r under the influence of centripetal force K/r 2 where K is a constant. Find total energy of the particle. 86.Explain why curved roads are generally banked? 87.Prove that acceleration due to gravity g on the surface of each is given by the expression 88.Two wires of same material and same length have diameters in the ratio of 1:2. If a load produces an extension of 8mm in first wire then find extension in second wire by this load. 89.Drive expression for centripetal force acting on a body describing a circular path with constant speed. 90.A cricket ball of mass 0.150kg moving with a speed of 12ms -1 is hit by a bat so that the ball is turned back with a velocity of 10ms -1. Force of the blow acts for 0.01s. Find the impulse received by the ball. What is the significance of: i. F-x graph ii. F-t graph. 91.Define escape velocity. Calculate escape velocity from surface of earth. Given M e = 5.98 x 10 24 kg. R e = 6.37 x 10 6 m and G = 6.67 x 10-11 S.I units. 92.A force F=(2i + 3j + 5k) N acts on a particle and displaces it through S = (4i j + 5k)m, calculate the work done. 93.What is Einstein s Energy Mass Equivalence relationship? Derive using relativistic mass formula calculate energy released from complete annihilation of 1g matte. If the energy of a body increases by 300% by what percentage does its momentum increase? When slow neutrons are incident on a target containing 235 U 92, a possible fission reaction is Estimate the amount of energy released using following data: M( = 235.04 amu M( ) = 140.91 amu M( ) = 91.926 amu M n = 1.0087 amu 94.What are the dimensions of Gravitational constant? 95.Name the physical quantity which is expressed as force time velocity. Is it a scalar or vector quantity? 96.What is different between mass and weight? 97.Why is the blood pressure in bumans greater at the feet than at the brain? 98.What is moment of inertia? Write its S.I unit. 99.A cricket ball of mass 500gm is moving with speed of 36kmh-1. It is reflected back with the same speed. What is the impulse applied on it? How will the time period of a simple pendulum change if its length is doubled?
100. How far away from the surface of earth does the acceleration due to gravity becomes 40% of its value on the surface of earth? Radius of earth = 6400km. 101. Verify dimensionally, the relation T = 102. A balloon is moving upward with a speed of 5ms -1. When it is at a heigth of 98m a packet is dropped from it. What is the velocity of the packet when it strikes the ground? 103. Define Angular velocity and Angular acceleration. Derive an expression for centripetal acceleration of uniform circular motion of an object. 104. A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw same ball? From the top of the tower 100m in height, a ball is dropped and at the same time another ball is projected vertically upwards from the ground with a velocity of 25ms -1. Find when and where the two balls will meet. (g = 9.8ms -2 ) 105. Define elastic and inelastic collision. A lighter body collides with a much more massive body at rest. Prove that the direction of lighter body reversed and massive body remains at rest. 106. Derive an expression for the apparent frequency when the source and observer are moving in the same direction with velocity v s and v 0 respectively, with source following the observer. State Newton s formula for velocity of sound in air. Point out the assumption and hence discuss Laplace s correction. 107. State and explain the law of conservation of energy. Show that the energy in case of a free fall of a body is conserved. i. State and prove the work-energy theorem. ii. Two spring A and B with constants Ka and Kb (Ka > Kb) are given. In which of the spring more work is to be done, if They are stretched by the same amount They are stretched by same force. <<<<<<<<<<<<ALL THE BEST>>>>>>>>>>>>