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The volume of a cube of side 1 cm is equal to ______ m3
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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.
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The industrial revolution in England and Western Europe more than two centuries ago was triggered by some key scientific and technological advances. What were these advances?
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A vehicle moving with a speed of 18 km h–1covers ______ m in 1 s.
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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:
- Atoms are very small objects
- A jet plane moves with great speed
- The mass of Jupiter is very large
- The air inside this room contains a large number of molecules
- A proton is much more massive than an electron
- The speed of sound is much smaller than the speed of light.
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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?
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A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m0 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/(1-v^2)^(1/2)`
Guess where to put the missing c.
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Fill in the blank by suitable conversion of unit:
1 kg m2s–2= ______ g cm2 s–2
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Fill in the blank by suitable conversion of unit:
1 m =______ ly
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Fill in the blank by suitable conversion of unit:
3.0 m s–2= ______ km h–2
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Fill in the blank by suitable conversion of unit:
G= 6.67 × 10–11 N m2 (kg)–2= ______ (cm)3s–2 g–1
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Young’s modulus of steel is 1.9 × 1011 N/m2. When expressed in CGS units of dynes/cm2, it will be equal to (1N = 105 dyne, 1m2 = 104 cm2)
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Photon is quantum of radiation with energy E = h ν where ν is frequency and h is Planck’s constant. The dimensions of h are the same as that of ______.
- Linear impulse
- Angular impulse
- Linear momentum
- Angular momentum
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During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.
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If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system of units?
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Give an example of a constant which has no unit.
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Calculate the solid angle subtended by the periphery of an area of 1 cm2 at a point situated symmetrically at a distance of 5 cm from the area.
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A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?
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The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?
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The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?
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