(c) 3.0 3 - .... 11
(d) G = 6.67 x 10-11 N m² (kg) 2 = .... (cm) s? g?.
23 A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kø m2 g-2
Suppose we employ a system of units in which the unit of mass equals a kg, the unit
of length equals B m, the unit of time is ys. Show that a calorie has a magnitude 4.)
a B-2 y2 in terms of the new units.
statement clearly :
Answers
(c) 1 hour = 3600 sec so that 1 sec = 1/3600 hour
1 km = 1000 m so that 1 m = 1/1000 km
3.0 m s–2 = 3.0 (1/1000 km)( 1/3600 hour)-2 = 3.0 × 10–3 km × ((1/3600)-2 h–2)
= 3.0 × 10–3 km × (3600)2 h–2 = 3.88 × 104 km h–2
3.0 m s–2= 3.88 × 104 km h–2
(d) Given,
G= 6.67 × 10–11 N m2 (kg)–2
We know that
1 N = 1 kg m s–2
1 kg = 103 g
1 m = 100 cm = 102 cm
Putting above values, we get
6.67 × 10–11 N m2 kg–2 = 6.67 × 10–11 × (1 kg m s–2) (1 m2) (1Kg–2)
Solve and cancel out the units we get
⇒ 6.67 × 10–11 × (1 kg–1 × 1 m3 × 1 s–2)
Putting above values to convert Kg to g and m to cm
⇒ 6.67 × 10–11 × (103 g)-1 × (102 cm)3 × (1 s–2)
⇒ 6.67 × 10–11 × 10-3 g-1 × 106 cm3 × (1 s–2)
⇒ 6.67 × 10–8 cm3 s–2 g–1
G= 6.67 × 10–11 N m2 (kg)–2= 6.67 × 10–8 (cm)3s–2 g–1.
2.3
Answer :
Given that,
1 Calorie=4.2 J = 4.2 Kg m2 s-2 ...... (i)
As new unit of mass = α Kg
∴ 1 Kg = 1/α new unit of mass
Similarly, 1 m = β-1 new unit of length
1 s = γ-1 new unit of time
Putting these values in (i), we get
1 calorie = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2
= 4.2 α-1 β-2 γ2 new unit of energy (Proved)
Solution
Given that,
1 Calorie=4.2 J = 4.2 Kg m2 s-2 …… (i)
As new unit of mass = α Kg
∴ 1 Kg = 1/α new unit of mass
Similarly, 1 m = β-1 new unit of length
1 s = γ-1 new unit of time
Putting these values in (i), we get
1 calorie = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2
= 4.2 α-1 β-2 γ2 new unit of energy (Proved)