The value of the universal gravitational constant is 6 . 67 × 10 - 11 N m 2 kg - 2 . Find its value in g - 1 cm 3 s - 2 .

As we know that : 1 N = 1 kg × ms - 2 So, 1 Nm 2 kg - 2 = 1 kg ms - 2 × m 2 kg 2 = 1 kg - 1 m 3 s - 2 And 1 kg = 10 3 g , 1 m = 10 2 cm therefore, 1 kg - 1 m 3 s - 2 = ( 10 3 g ) - 1 × ( 10 2 c m ) 3 s - 2 = 10 - 3 g - 1 × 10 6 cm 3 s - 2 Hence 1 kg - 1 m 3 s - 2 = 10 3 g - 1 cm 3 s - 2 The value of G = 6 . 6 × 10 - 11 × 10 3 g - 1 cm 3 s - 2 = 6 . 67 × 10 - 8 gm - 1 cm 3 s - 2

The value of Stefan's constant is σ = 5 . 67 × 10 - 5 ergs - 1 cm - 2 K - 4 . Find its value in SI units.

As we know that: 1 erg = 10 - 7 J and 1 m = 100 cm Therefore, substituting these values, we have the stephan's constant in S I units: σ = 5 . 67 × 10 - 5 ergs - 1 cm - 2 K - 4 = 5 . 67 × 10 - 5 × 10 - 7 Js - 1 ( 10 - 2 m ) - 2 K - 4 σ = 5 . 67 × 10 - 8 J s - 1 m - 2 K - 4

Express speed of light ( 3 . 0 × 10 8 m / s ) in terms of AU per min.

Astronomical unit A U is used to measure large distances in space. Following are the conversion factors for the various units 1 km = 1000 m 1 AU = 1 . 5 × 10 8 km 1 min = 60 s Thus, using the above relations the speed of light c = 3 × 10 8 meter / s can be written as: c = 3 × 10 8 m s = 3 × 10 8 1000 kms - 1 = 3 × 10 8 1000 × 1 . 5 × 10 8 60 1 = 0 . 12 AU / min

E M B I B E

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 4

EASY

11th ICSE

IMPORTANT

Earn 100

Find the number of hydrogen atoms required to obtain $1 kg$ of hydrogen. The mass of one hydrogen atom = $1 U = 1.66 \times 10^{- 27} kg$ .

Important Questions on Units : Fundamental and Derived Units

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 5

The earth has a mass of

5.98 \times 10^{24} k g .

The average mass of the atom of the earth is

40 u

. How many atoms are in the earth?

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 6

The density of water at

4 ° C

is

1.00 g / {cm}^{3}

. Find its value in SI units.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 7

The acceleration of a body is

10 m / s^{2}

. Express it in

km / h^{2} .

HARD

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 8

The value of the universal gravitational constant is

6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

. Find its value in

g^{- 1} {cm}^{3} s^{- 2}

.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 9

The value of Stefan's constant is

σ = 5.67 \times 10^{- 5} {ergs}^{- 1} {cm}^{- 2} K^{- 4}

. Find its value in SI units.

MEDIUM

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 10

Express speed of light

(3.0 \times 10^{8} m / s)

in terms of AU per min.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 11

If the speed of light is new unit of speed and year is the new unit of time. Then what is the new unit of length? What is its name? Given that

c = 3 \times 10^{8} m / s

and year=

3.154 \times 10^{7} \sec .

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 2 - Units : Fundamental and Derived Units>NUMERICALS>Q 12

For a new unit of length, the speed of radio wave is unity. Find the distance of an aircraft from a RADAR, if the radio signals return back after reflection of aircraft in