Question

Question 2.3 A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–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 γ2 in terms of the new units.

Class XI Physics Units And Measurements Page 35

Answer 1

Hello



1 calorie = 4.2 j
1J = 1 kg m2s–2
put the value we get =>

1 calorie =4.2 kg m2s–2 = 4.2 × (1 kg) × (1 m2) × (1 s–2) …(1)
Given that
Unit of mass equals α kg => 1 kg mass = 1/α mass
Unit of length equals β m => 1 m length = 1/ β length
Unit of time is γs => 1 s time = 1/ γ time
Put the values in equation (1), we get
New unit of mass = α kg
=4.2 × (1 kg) × (1 m2) × (1 s–2)
= 4.2 × (1/ α ) × (1/ β ) 2 × (1/ γ) –2
= 4.2 × ( α–1 ) × (β–1 ) 2 × ( γ–1) –2
=4.2 α–1 β–2 γ2

Answer 2

Answer:

Explanation:

Solution,

Here, we have

1 calorie = 4.2 (1 kg) (1 m²) (1 s⁻²)

Here, we will change all units,

New unit of mass = α kg

in terms of the new unit, 1 kg

⇒ 1 kg = 1/α

⇒ 1 kg = α⁻¹

Now, In terms of the new unit of length,

⇒ 1 m = 1/β

⇒ 1 m = β⁻¹

⇒ 1 m² = β⁻²

Now, In terms of the new unit of time,

⇒ 1 s = 1/γ

⇒ 1 s = γ⁻¹

⇒ 1 s² = γ⁻²

⇒ 1 s⁻² = γ²

Here, we get

⇒ 1 calorie = 4.2 (1 α⁻¹) (1 β⁻²) (1 γ²)

1 calorie = 4.2 α⁻¹ β⁻² γ².