Fill in the blanks

The volume of a cube of side 1 cm is equal to.....m^{3}

Concept: International System of Units

Fill in the blanks

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

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/(1-v^2)^(1/2)`

Guess where to put the missing c.

Concept: International System of Units

Fill in the blanks by suitable conversion of units: 1 kg m^{2}s^{–2}= ....g cm^{2} s^{–2}

Concept: International System of Units

Fill in the blanks by suitable conversion of units:

3.0 m s^{–2}=.... km h^{–2}

Concept: International System of Units

Fill in the blanks by suitable conversion of units:

G= 6.67 × 10^{–11} N m^{2} (kg)^{–2}=.... (cm)^{3}s^{–2} g^{–1}.

Concept: International System of Units

Young’s modulus of steel is 1.9 × 10^{11} N/m^{2}. When expressed in CGS units of dynes/cm^{2}, it will be equal to (1N = 10^{5} dyne, 1m^{2} = 10^{4} cm^{2})

Concept: International System of Units

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

Concept: International System of Units

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.

Concept: International System of Units

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?

Concept: International System of Units

Give an example of a constant which has no unit.

Concept: International System of Units

Calculate the solid angle subtended by the periphery of an area of 1 cm^{2} at a point situated symmetrically at a distance of 5 cm from the area.

Concept: International System of Units

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?

Concept: International System of Units

A vehicle moving with a speed of 18 km h^{–1}covers....m in 1 s

Concept: Measurement of Length

Which of the following is the most precise device for measuring length:

(a) a vernier callipers with 20 divisions on the sliding scale

(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(c) an optical instrument that can measure length to within a wavelength of light ?

Concept: Measurement of Length

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by `Å: 1Å = 10^(-10)m` . The size of a hydrogen atom is about 0.5Å. what is the total atomic volume in m^{3} of a mole of hydrogen atoms?

Concept: Measurement of Length

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?

Concept: Measurement of Length