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The volume of a cube of side 1 cm is equal to.....m^{3}
Concept: International System of Units
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The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ... (mm)^{2}
Concept: International System of Units
Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?
Concept: Concept of Physics
“Every great physical theory starts as a heresy and ends as a dogma”. Give some examples from the history of science of the validity of this incisive remark
Concept: Concept of Physics
“Politics is the art of the possible”. Similarly, “Science is the art of the soluble”. Explain this beautiful aphorism on the nature and practice of science.
Concept: Concept of Physics
India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?
Concept: Concept of Physics
“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.
Concept: Concept of Physics
A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m^{2}s^{–2}. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^{–1} β^{–2} γ^{2 }in terms of the new units.
Concept: International System of Units
Explain this statement clearly:
“To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(a) atoms are very small objects
(b) a jet plane moves with great speed
(c) the mass of Jupiter is very large
(d) the air inside this room contains a large number of molecules
(e) a proton is much more massive than an electron
(f) the speed of sound is much smaller than the speed of light.
Concept: International System of Units
A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?
Concept: International System of Units
A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m_{0} of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:
`m = m_0/(1v^2)^(1/2)`
Guess where to put the missing c.
Concept: International System of Units
In which of the following examples of motion, can the body be considered approximately a point object:
(a) a railway carriage moving without jerks between two stations.
(b) a monkey sitting on top of a man cycling smoothly on a circular track.
(c) a spinning cricket ball that turns sharply on hitting the ground.
(d) a tumbling beaker that has slipped off the edge of a table.
Concept: Position, Path Length and Displacement
The positiontime (xt) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Figure Choose the correct entries in the brackets below;
(a) (A/B) lives closer to the school than (B/A)
(b) (A/B) starts from the school earlier than (B/A)
(c) (A/B) walks faster than (B/A)
(d) A and B reach home at the (same/different) time
(e) (A/B) overtakes (B/A) on the road (once/twice).
Concept: Position, Path Length and Displacement
A woman starts from her home at 9.00 am, walks with a speed of 5 km h^{–1} on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 km h^{–1}. Choose suitable scales and plot the xt graph of her motion.
Concept: Position, Path Length and Displacement
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the xtgraph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
Concept: Position, Path Length and Displacement
Read each statement below carefully and state with reasons and examples, if it is true or false;
A particle in onedimensional motion with zero speed at an instant may have nonzero acceleration at that instant
Concept: Position, Path Length and Displacement
Read each statement below carefully and state with reasons and examples, if it is true or false;
A particle in onedimensional motion with zero speed may have nonzero velocity,
Concept: Position, Path Length and Displacement
Read each statement below carefully and state with reasons and examples, if it is true or false;
A particle in onedimensional motion with constant speed must have zero acceleration
Concept: Position, Path Length and Displacement
Read each statement below carefully and state with reasons and examples, if it is true or false;
A particle in onedimensional motion with positive value of acceleration mustbe speeding up.
Concept: Position, Path Length and Displacement
Explain clearly, with examples, the distinction between:
 Magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval.

Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.
When is the equality sign true? [For simplicity, consider onedimensional motion only].
Concept: Position, Path Length and Displacement