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Welcome to Paul’s Coaching Global — the ultimate hub for Class 11 CBSE Science. This page is SEO-optimized and designed with funky flash effects to keep learning exciting.
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Physics Lab
Q1. A particle moves in a circle of radius 2 m with constant speed 4 m/s. Find its acceleration.
(2 marks)
Q2. A body of mass 5 kg is acted upon by a force of 20 N. Calculate its acceleration.
(2 marks)
Q3. Derive the expression for kinetic energy in terms of momentum.
(3 marks)
Physics Lab: Motion & Laws
Q1. A car moving with a speed of 50 km/h can be stopped by brakes over a distance of 6 m. If the same car is moving at 100 km/h, what is the minimum stopping distance? (Assume constant retardation)
(2 marks)
Q2. The position of an object is given by x = 3t² – 4t + 5. Find its velocity and acceleration at t = 2 s.
(2 marks)
Q3. Can an object have a constant speed but a variable velocity? Explain with an example.
(2 marks)
Q4. Draw the position-time graph for two objects moving with positive velocities, where the relative velocity of A with respect to B is zero.
(2 marks)
Q5. A ball is thrown vertically upwards. What is the velocity and acceleration of the ball at the highest point of its motion?
(2 marks)
Q6. Explain why the speed of a projectile is minimum at the highest point of its trajectory.
(2 marks)
Q7. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How high above the ground can the cricketer throw the same ball?
(2 marks)
Q8. What is the angle between velocity and acceleration in uniform circular motion? Justify your answer.
(2 marks)
Q9. Two vectors A and B are such that |A + B| = |A – B|. What is the angle between vectors A and B?
(2 marks)
Q10. A boatman wants to reach a point just opposite on the other bank of a river. If the speed of the boat in still water is greater than the speed of the river flow, in which direction should he row the boat?
(2 marks)
Q11. Why does a person sitting in a moving bus fall forward when the bus suddenly stops? State the law involved.
(2 marks)
Q12. A bullet of mass 20 g is fired from a pistol of mass 2 kg with a velocity of 150 m/s. What is the recoil velocity of the pistol?
(2 marks)
Q13. State the principle of conservation of linear momentum. Show that it is a consequence of Newton’s second and third laws of motion.
(2 marks)
Q14. Why is it easier to pull a lawn roller than to push it? Explain with a diagram.
(2 marks)
Q15. Define impulse. How is it related to the change in momentum?
(2 marks)
Physics Lab: Rotational Motion & Gravitation
Q16. A block of mass ‘m’ is placed on a rough inclined plane of inclination θ. What is the minimum force required to just move the block up the plane?
(2 marks)
Q17. Explain the concept of banking of roads. Why is it necessary?
(2 marks)
Q18. A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string?
(2 marks)
Q19. Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses. (g = 10 m/s²)
(2 marks)
Q20. Friction is a necessary evil. Justify this statement with two examples for each case.
(2 marks)
Q21. Why are spokes fitted in a bicycle wheel? Explain on the basis of moment of inertia.
(2 marks)
Q22. State the theorem of parallel axes and the theorem of perpendicular axes for moment of inertia.
(2 marks)
Q23. A solid sphere and a hollow sphere of the same mass and radius are allowed to roll down an inclined plane from the same height. Which one will reach the bottom first? Why?
(2 marks)
Q24. What is the physical significance of the radius of gyration?
(2 marks)
Q25. A flywheel rotating at 420 rpm slows down at a constant rate of 2 rad/s². What time is required to stop the flywheel?
(2 marks)
Q26. Establish the relation between torque and angular momentum for a rigid body.
(2 marks)
Q27. A child is sitting on a revolving chair with his arms outstretched. What will happen to his angular speed if he folds his arms? Explain why.
(2 marks)
Q28. A solid cylinder of mass 20 kg rotates about its axis with an angular speed of 100 rad/s. The radius of the cylinder is 0.25 m. What is the rotational kinetic energy of the cylinder?
(2 marks)
Q29. Define the centre of mass. Can the centre of mass of a body lie outside the body? Give an example.
(2 marks)
Q30. A meter stick is balanced on a knife-edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the meter stick?
(2 marks)
Gravitation & Satellites
Q31. State Kepler’s laws of planetary motion.
(2 marks)
Q32. Why does the Moon have no atmosphere?
(2 marks)
Q33. What is escape velocity? Derive an expression for the escape velocity of an object from the surface of the Earth.
(2 marks)
Q34. If the radius of the Earth were to shrink by 1%, its mass remaining the same, what would be the change in the value of ‘g’ on the surface of the Earth?
(2 marks)
Q35. What is a geostationary satellite? State its essential conditions.
(2 marks)
Q36. Explain how the value of ‘g’ varies with depth below the surface of the Earth.
(2 marks)
Q37. Define gravitational potential energy. Is it a scalar or a vector quantity?
(2 marks)
Q38. An object weighs 72 N on the surface of the Earth. What is its weight at a height of R/2 from the surface of the Earth? (R = radius of Earth)
(2 marks)
Q39. What is the time period of a simple pendulum inside a satellite orbiting the Earth? Give a reason.
(2 marks)
Q40. Two artificial satellites are revolving in the same circular orbit. What is the ratio of their orbital speeds?
(2 marks)
Q41. The displacement of a particle is zero at t=0 and it is x at t=t. It starts moving in the positive x-direction with a velocity which varies as v = k√x. How does the displacement depend on time?
(2 marks)
Q42. A car accelerates from rest at a constant rate a for some time, after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t, find the maximum velocity achieved.
(2 marks)
Q43. The range of a projectile is the same when its maximum heights are h₁ and h₂. Find the relation between the range R and the heights h₁ and h₂.
(2 marks)
Q44. A man can swim with a speed of 4 km/h in still water. How long does he take to cross a river 1 km wide if the river flows steadily at 3 km/h and he makes his strokes normal to the river current?
(2 marks)
Q45. A block rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, what is the mass of the block? (g = 10 m/s²)
(2 marks)
Advanced Mechanics
Q46. A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
(2 marks)
Q47. A bomb at rest explodes into three fragments of equal masses. Two fragments fly off at right angles to each other with velocities 9 m/s and 12 m/s respectively. Calculate the speed of the third fragment.
(2 marks)
Q48. A disc of radius R is rotating with an angular speed ω₀ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is μₖ. What is the time when it starts pure rolling?
(2 marks)
Q49. A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
(2 marks)
Q50. A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (Kₜ) as well as rotational kinetic energy (Kᵣ) simultaneously. What is the ratio Kₜ : Kᵣ for the sphere?
(2 marks)
Q51. The moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is I. What is its moment of inertia about a tangent parallel to its diameter?
(2 marks)
Q52. A particle performs uniform circular motion with an angular momentum L. If its angular frequency is doubled and its kinetic energy is halved, what happens to the angular momentum?
(2 marks)
Q53. The angular momentum of a particle is given by L = (6t² i – 3t j + 4 k) J-s. Find the torque acting on the particle at t = 1 s.
(2 marks)
Q54. The distance of two planets from the Sun are 10¹³ m and 10¹² m respectively. Find the ratio of their time periods.
(2 marks)
Q55. At what height from the surface of the Earth will the value of ‘g’ be reduced by 36% from the value at the surface? (Radius of Earth = R)
(2 marks)
Q56. The escape velocity from the Earth’s surface is 11.2 km/s. If the mass of a planet is 100 times that of Earth and its radius is 4 times that of Earth, what will be the escape velocity from the planet’s surface?
(2 marks)
Q57. A satellite is orbiting the Earth at a height of 3R from its surface, where R is the radius of the Earth. What is the orbital speed of the satellite?
(2 marks)
Q58. Define gravitational potential. Show that the gravitational potential at a point is always negative.
(2 marks)
Q59. A body is projected vertically upwards from the surface of the Earth with a velocity equal to half of the escape velocity. What is the maximum height reached by the body?
(2 marks)
Q60. If the Earth stops rotating about its axis, what will be the effect on the value of ‘g’ at the poles and at the equator?
(2 marks)
Assertion–Reasoning Arena
Instructions: For each question, choose one of the following options:
- a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
- c) Assertion is true but Reason is false.
- d) Both Assertion and Reason are false.
Q1. Assertion: The displacement of a body may be zero, even when its distance is not zero. Reason: Displacement is the shortest path between the initial and final points, whereas distance is the total path length.
(2 marks)
Q2. Assertion: A body can have acceleration even if its velocity is zero at a given instant. Reason: A body is momentarily at rest when it reverses its direction of motion.
(2 marks)
Q3. Assertion: The speed of a projectile at its maximum height is half of its initial speed of projection. Reason: At the maximum height, only the horizontal component of velocity exists.
(2 marks)
Q4. Assertion: The angle between the instantaneous velocity and acceleration of a particle in projectile motion is never zero. Reason: The acceleration in projectile motion is always directed vertically downwards.
(2 marks)
Q5. Assertion: In uniform circular motion, the acceleration of the particle is zero. Reason: The speed of the particle in uniform circular motion is constant.
(2 marks)
Q6. Assertion: A vector quantity has both magnitude and direction and obeys the triangle law of addition. Reason: A current has both magnitude and direction, but it is a scalar quantity.
(2 marks)
Q7. Assertion: Frictional forces are conservative forces. Reason: Frictional force is always directed opposite to the direction of motion.
(2 marks)
Q8. Assertion: A cricketer moves his hands backwards while catching a ball. Reason: This increases the time of impact, and hence reduces the force exerted by the ball on the hands.
(2 marks)
Q9. Assertion: The work done by the centripetal force is always zero. Reason: The centripetal force is always perpendicular to the displacement.
(2 marks)
Q10. Assertion: Action and reaction forces do not cancel each other. Reason: Action and reaction forces act on two different bodies.
(2 marks)
Assertion–Reasoning Arena (Part 2)
Q11. Assertion: The centre of mass of a rigid body always lies inside the body. Reason: The centre of mass is a point where the entire mass of the body is supposed to be concentrated.
(2 marks)
Q12. Assertion: The moment of inertia of a body is a measure of its rotational inertia. Reason: The moment of inertia depends on the mass of the body and its distribution about the axis of rotation.
(2 marks)
Q13. Assertion: When a body is rolling, the frictional force acts in the forward direction. Reason: Rolling friction is a self-adjusting force.
(2 marks)
Q14. Assertion: The angular momentum of a planet revolving around the sun is conserved. Reason: The gravitational force of the sun on the planet is a central force, so its torque is zero.
(2 marks)
Q15. Assertion: A solid sphere and a hollow sphere of the same mass and radius will have the same moment of inertia about their diameters. Reason: The distribution of mass is different in solid and hollow spheres.
(2 marks)
Q16. Assertion: The value of acceleration due to gravity ‘g’ is different at poles and equator. Reason: The Earth is flattened at the poles and bulges at the equator.
(2 marks)
Q17. Assertion: The time period of a satellite revolving close to the Earth’s surface is independent of its mass. Reason: The orbital velocity is independent of the mass of the satellite.
(2 marks)
Q18. Assertion: A person in a freely falling lift experiences weightlessness. Reason: The normal reaction from the floor of the lift on the person is zero.
(2 marks)
Q19. Assertion: Gravitational potential is a vector quantity. Reason: Gravitational potential is defined as the work done per unit mass.
(2 marks)
Q20. Assertion: Kepler’s second law of planetary motion is a consequence of the law of conservation of angular momentum. Reason: The gravitational force is a central force, so the torque on the planet is zero.
(2 marks)
Assertion–Reasoning Arena (Part 3)
Q21. Assertion: The velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis. Reason: In uniform motion, the velocity of the object increases uniformly with time.
(2 marks)
Q22. Assertion: The range of a projectile is maximum for a projection angle of 45°. Reason: The range is given by R = (u² sin 2θ) / g.
(2 marks)
Q23. Assertion: It is difficult to move a cycle along a road with its brakes on. Reason: Sliding friction is greater than rolling friction.
(2 marks)
Q24. Assertion: A rocket works on the principle of conservation of linear momentum. Reason: For a system with no external force, the linear momentum is constant.
(2 marks)
Q25. Assertion: The centre of mass of a two-particle system lies on the line joining the two particles. Reason: The position vector of the centre of mass is given by R = (m₁r₁ + m₂r₂) / (m₁ + m₂).
(2 marks)
Q26. Assertion: Torque is an axial vector. Reason: The direction of torque is perpendicular to the plane containing the position vector and the force.
(2 marks)
Q27. Assertion: If the radius of the Earth is halved, keeping its mass constant, the escape velocity will become 12 times. Reason: Escape velocity is inversely proportional to the square root of the radius of the Earth.
(2 marks)
Q28. Assertion: The binding energy of a satellite is the energy required to remove it from its orbit to infinity. Reason: The total energy of an orbiting satellite is negative.
(2 marks)
Q29. Assertion: A body cannot be in equilibrium if only a single force acts on it. Reason: For equilibrium, the net force on the body must be zero.
(2 marks)
Q30. Assertion: The moment of inertia of a steel sphere is greater than the moment of inertia of a wooden sphere of the same radius. Reason: The density of steel is greater than that of wood.
(2 marks)
Case Study Hub
Case Study 1: Projectile Motion
A projectile is an object thrown into the air, subject to only the acceleration of gravity. The path followed by a projectile is called its trajectory, which is a parabola.
- (a) At what angle of projection is the horizontal range of a projectile maximum? i) 30° ii) 45° iii) 60° iv) 90°
- (b) For a projectile, the ratio of maximum height reached to the square of flight time is: i) 5 : 4 ii) 5 : 2 iii) g : 8 iv) g : 4
- (c) A cricketer throws a ball with a velocity of 20 m/s at an angle of 30° with the horizontal. What is the maximum height attained? (g = 10 m/s²) i) 5 m ii) 10 m iii) 15 m iv) 20 m
- (d) The speed of a projectile at its maximum height is half its initial speed. The angle of projection is: i) 30° ii) 45° iii) 60° iv) 90°
- (e) A projectile is given an initial velocity of (i + 2j) m/s. The equation of its trajectory is (g = 10 m/s²): i) y = 2x – 5x² ii) y = x – 5x² iii) 4y = 2x – 5x² iv) 4y = x – 5x²
Case Study 2: Satellites and Gravitation
Satellites revolve around planets in fixed orbits governed by gravitation. Their orbital velocity, time period, and energy depend on mass and radius of orbit.
- (a) The orbital velocity of a satellite revolving close to the Earth’s surface is approximately: i) 11.2 km/s ii) 7.9 km/s iii) 3.1 km/s iv) 9.8 m/s
- (b) If the height of a satellite’s orbit from the Earth’s surface is increased, its time period will: i) decrease ii) increase iii) remain the same iv) become zero
- (c) The total energy of a circularly orbiting satellite is: i) twice the kinetic energy ii) half the kinetic energy iii) equal to the negative of its kinetic energy iv) equal to the negative of its potential energy
- (d) Two satellites A and B have masses m and 2m in circular orbits of radii R and 2R respectively. The ratio of their orbital speeds (Vₐ/Vb) is: i) 1 ii) 2 iii) √2 iv) 1/√2
- (e) A geostationary satellite revolves around the Earth in an orbit that is: i) circular and in the equatorial plane ii) elliptical and in the equatorial plane iii) circular and in a polar plane iv) elliptical and in a polar plane
Case Study Hub
Case Study 1: Projectile Motion
A projectile is an object thrown into the air, subject to only the acceleration of gravity. The path followed by a projectile is called its trajectory, which is a parabola.
- (a) At what angle of projection is the horizontal range of a projectile maximum? i) 30° ii) 45° iii) 60° iv) 90°
- (b) For a projectile, the ratio of maximum height reached to the square of flight time is: i) 5 : 4 ii) 5 : 2 iii) g : 8 iv) g : 4
- (c) A cricketer throws a ball with a velocity of 20 m/s at an angle of 30° with the horizontal. What is the maximum height attained? (g = 10 m/s²) i) 5 m ii) 10 m iii) 15 m iv) 20 m
- (d) The speed of a projectile at its maximum height is half its initial speed. The angle of projection is: i) 30° ii) 45° iii) 60° iv) 90°
- (e) A projectile is given an initial velocity of (i + 2j) m/s. The equation of its trajectory is (g = 10 m/s²): i) y = 2x – 5x² ii) y = x – 5x² iii) 4y = 2x – 5x² iv) 4y = x – 5x²
Case Study 2: Satellites and Gravitation
Satellites revolve around planets in fixed orbits governed by gravitation. Their orbital velocity, time period, and energy depend on mass and radius of orbit.
- (a) The orbital velocity of a satellite revolving close to the Earth’s surface is approximately: i) 11.2 km/s ii) 7.9 km/s iii) 3.1 km/s iv) 9.8 m/s
- (b) If the height of a satellite’s orbit from the Earth’s surface is increased, its time period will: i) decrease ii) increase iii) remain the same iv) become zero
- (c) The total energy of a circularly orbiting satellite is: i) twice the kinetic energy ii) half the kinetic energy iii) equal to the negative of its kinetic energy iv) equal to the negative of its potential energy
- (d) Two satellites A and B have masses m and 2m in circular orbits of radii R and 2R respectively. The ratio of their orbital speeds (Vₐ/Vb) is: i) 1 ii) 2 iii) √2 iv) 1/√2
- (e) A geostationary satellite revolves around the Earth in an orbit that is: i) circular and in the equatorial plane ii) elliptical and in the equatorial plane iii) circular and in a polar plane iv) elliptical and in a polar plane
⚡ Final Boss Arena ⚡
The Ultimate Challenge — Only the Brave Conquer!
Q61. A satellite is launched from Earth with velocity greater than escape velocity. Describe its motion and fate.
(3 marks)
Q62. A solid sphere, a hollow sphere, and a cylinder of the same mass and radius are released from the same height on an inclined plane. Which will reach first? Justify with energy considerations.
(3 marks)
Q63. Derive the expression for orbital velocity of a satellite in terms of Earth’s radius and gravitational constant.
(3 marks)
Q64. A projectile is fired at an angle θ with velocity u. Derive the equation of its trajectory and show it is parabolic.
(3 marks)
Q65. A body of mass 10 kg is rotating with angular velocity 20 rad/s. Calculate its angular momentum if its radius of gyration is 0.5 m.
(3 marks)
Q66. Explain why astronauts feel weightlessness in a satellite even though gravity is acting on them.
(2 marks)
Q67. A rocket of mass 1000 kg expels gas at 500 m/s. Calculate the acceleration of the rocket when the rate of mass ejection is 10 kg/s.
(3 marks)
Q68. A pendulum clock is taken to the top of a mountain. Will it gain or lose time? Explain with reference to variation of g.
(2 marks)
Q69. A disc of mass 2 kg and radius 0.2 m is rolling without slipping with velocity 5 m/s. Calculate its total kinetic energy.
(3 marks)
Q70. A geostationary satellite is launched at a height of 36,000 km. Explain why its time period is 24 hours and why it appears stationary.
(3 marks)
Biology Arena
Q16. Explain the structure of DNA with a neat diagram.
(3 marks)
Q17. Differentiate between mitosis and meiosis with at least two points each.
(2 marks)
Q18. Describe the fluid mosaic model of the cell membrane.
(3 marks)
Q19. Explain the role of ribosomes in protein synthesis.
(2 marks)
Q20. What are enzymes? Explain their mode of action with an example.
(3 marks)
Q21. Define photosynthesis and write its balanced chemical equation.
(2 marks)
Q22. Explain the difference between aerobic and anaerobic respiration.
(2 marks)
Q23. Describe Mendel’s law of segregation with an example.
(3 marks)
Q24. What is osmosis? Give one example from plant cells.
(2 marks)
Q25. Explain the structure and function of mitochondria.
(3 marks)