QUESTIONS

Chapter 1 : Scalars and Vectors

1. Distinguish between scalars and vectors, give examples of each.

2. Find the work done by the force (Newton) when displacement is (meter).

   Ans : 56 Joules.

3. A particle of mass 2 kg is located at a particular instant at the point P(2, 3, 5). The co-ordinates are measured in meters. If the velocity of the particle is (m /s) then find the linear and angular momentum of the particle at that instant.

   Ans :
           

4. Show that the area of a parallelogram whose two co-terminus sides are and . The sides are measured in meters.

   Ans : 51.4 m²

5. Find the volume of a parallelepiped whose three co-terminus sides are, in meters.

   Ans : 64 m³

Chapter : 2 Kinematics

1. An object travels along a straight line. It covers 50 m in the first ten seconds and 100 m in the next ten seconds. What is its average speed ?

   Ans : 7.5 m/s

2. An object traveling along a straight line covers the first half of the journey with speed u₁ and the next half of the journey with speed u₂ . Show that its average speed is 2u₁u₂ / (u₁) + u₂) .

3. An object thrown upwards from the ground returns to the ground in 10 sec. Find the speed with which it was thrown up and the maximum height to which it can rise. (g = 9.8 m/s² ).

   Ans : 49 m/s and 122.5 m.

4. The velocity of an object moving along a straight line path is represented graphically as shown.

   

   Click here to enlarge

   Find :

   (i)    The total distance traveled,

   (ii)   Average velocity in 10 sec. interval,

   (iii) Accelerations in OA, AB, BC, CD, DE parts of        motion.

   Ans : (i) 70 m (ii) 7 m/s (iii) 10 m/s2 , zero, - 5/3 m/s², zero, - 5 m/s²

5. A monkey is sitting on a tree along the line of sight of a rifle aimed at it. The moment the rifle is fired, the monkey just jumps off in a vertical direction. Will the bullet hit the monkey ? Justify your answer.

   Ans : Yes, The monkey falls to the position of maximum height of bullet simultaneously.

6. A simple pendulum of length 1 m is held in the horizontal position initially, and then it is released. Find the tension in the string at any position and show that the bob has three times its normal weight when it is in the lowest position.

   Ans : Tension in any position is T = 3mg sin q and T_lowest = 3mg as q = 90⁰

Chapter 3 : Dynamics

1. Find the minimum force with which an object of mass 2 kg should be pressed against a rough vertical wall if the coefficient of static friction between the object and the wall is 0.5. If force greater than this minimum force is exerted will the object rise up along the wall. Explain ?

   (g = 9.8 m/s²)

   Ans : 39.2 N, No, the maximum force of friction cannot exceed driving force.

2. You are standing on a skating board on a perfectly smooth ice surface. How will you impart motion to the skating board ? Explain.

   Ans : Just by sitting away from the board, due to momentum conservation the board will move in the opposition direction.

3. Aeroplanes in flight usually follow the geodesic path i.e. arc of a circle whose center is same as that of the earth. A satellite in an ideal circular orbit is weightless. Why does weightlessness not occur in an aeroplane ?

   Ans : An Aeroplane's motion is not a 'free fall' motion whereas a satellite's motion is 'free fall' motion.

4. The moon revolves around the earth in (assumed) circular orbit. Draw a neat labelled diagram and indicate the following in it.

   (i) centripetal force

   (ii) centrifugal force

   (iii) centrifugal reaction

   (iv) Inertial frame of reference.

   (v) Non-inertial frame of reference.

5. Estimate the mass of the sun if the earth revolves in an (assumed) circular orbit of radius 150 million kilometers around the sun. Take period of the earth's revolution to be 365 days and

   G = 6.67 ´ 10^-11 N ´ m² / Kg² .

   Ans : 2.001 ´ 10³⁰ Kg

6. Three identical objects each of mass m kg are placed one at each vertex of an equilateral triangle of sides l . Show that the centre of mass of the system coincides with the centroid of the triangle. If one of the masses is 2 m, then explain how the center of mass (C.M.) will shift from its earlier position.

   Ans : It will shift towards the 2m mass.

7. Two identical spheres of same mass, approach each other with equal speeds along a straight line and undergo head-on elastic collision. What will be their velocities after the collision ? In the entire process, what is the state of motion of the C.M. of the system ?

   Ans : Velocities will just be reversed in direction only. The C.M. will remain at rest throughout.

Chapter 4 : Work, Energy and Power

1. A man walking on a levelled horizontal road, carries a heavy load kept on his head. Is he doing work or not ? Explain .

   Ans : He is not doing any work. Force and displacement are perpendicular to each other.

2. An object is set into motion on a rough horizontal road. What happens to its speed as time goes on? Is its K.E. lost ? Is it converted into some other form of energy or not ? If so in which form ?

   Ans : The speed of the object decreases. Yes. Yes. It is converted into Heat energy.

Chapter 5 : Rotational Motion

1. Does force of friction always oppose motion? Can it be a cause of motion ? Explain with examples.

   Ans : No. Yes, e.g. static force of friction can produce rotational motion.

2. If a ring, a disc, a sphere all of same mass and radius initially at rest on top of an inclined plane(rough) are released then the order in which they arrive earliest, later and latest is sphere, disc, ring respectively. Why is this so ? Explain.

1. Consider a rubber string and a steel wire of the same length. Which of them would be more elastic of the two? Explain.

2. Explain the variation of stress with respect to strain in terms of intramolecular forces.

3. A steel wire of length 2m is hanging from a rigid horizontal support. How much energy is stored in it when a load of 5 Kg is suspended on it ? If the load is increased to 10 Kg then by how much the energy stored will increase ? Y = 2 ´ 10¹¹ N/m², A = Area of cross section = 10^-6 m²

   Ans : 1.2 ´ 10^-2 Joule, 3.6 ´ 10^-2 Joule

4. An enclosed mass of ideal gas has isothermal bulk modulus equal to its pressure, and has adiabatic bulk modulus equal to Y times pressure where Y = ratio of molar Cp to Cv of the gas. State true or false and justify your answer.

Chapter 7 : Oscillatory Motion

1. Give some examples of oscillatory motions.

2. If a simple pendulum has total swing of 60⁰, is its motion oscillatory, is it also S.H. M. explain.

   Ans : The motion is oscillatory but not S.H.M. as the arc cannot be approximated to chord.

3. The bob of a simple pendulum is a hollow sphere with a hole at its bottom. It is completely filled with water and the hole is covered with a finger initially. It is deflected through an angle and released, simultaneously the finger is removed. Describe the variation in the period of the pendulum; give reasons for your answer.

   Ans : As the water starts flowing out the C.M. of the bob is lowered and again comes back to center when the bob is empty. Therefore l and hence T increases and then decreases back to original.

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Index

Questions
Bibilography

Chapter 1