Chapter 1 : Scalars and Vectors
Distinguish between scalars and vectors, give examples of each.
Find the work done by the force (Newton) when displacement
Ans : 56 Joules.
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.
Show that the area of a parallelogram whose two co-terminus sides are and . The sides are measured in meters.
Ans : 51.4
Find the volume of a parallelepiped whose three co-terminus sides are, in meters.
Ans : 64 m3
Chapter : 2 Kinematics
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
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) .
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
Ans : 49 m/s and 122.5 m.
The velocity of an object moving along a straight line path is represented graphically as shown.
Click here to enlarge
(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
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.
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 Tlowest = 3mg as q = 900
Chapter 3 : Dynamics
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
Ans : 39.2 N, No, the maximum force of friction cannot exceed driving force.
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.
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
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.
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
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.
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
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.
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
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.
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.
6 : Elasticity
Consider a rubber string and a steel wire of the same length. Which of them would be more elastic of the two? Explain.
Explain the variation of stress with respect to strain in terms of intramolecular forces.
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 =
Ans : 1.2
´ 10-2 Joule, 3.6 ´ 10-2 Joule
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
- Give some examples of oscillatory motions.
- 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.
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