Physics, asked by gaurav3627, 11 months ago

(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

Answered by jack6778
8

(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)

Answered by Aastha6878
1

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)

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