Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Theory of Relativity Reveals that Mass Can Be Converted into Energy. the Energy E So Obtained is Proportional to Certain Powers of Mass - Physics

Sum

Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions.

#### Solution

According to the theory of relativity, E α macb
⇒ E = kmacb, where k = proportionality constant

Dimension of the left side, [E] = [ML2T−2]

Dimension of the right side, [macb]= [M]a [LT−1]b

Equating the dimensions of both sides, we get:
[ML2T−2] = [M]a [LT−1]b
⇒ a = 1, b = 2
∴ E = kmc2

Concept: What is Physics?
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Chapter 1: Introduction to Physics - Exercise [Page 10]

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 15 | Page 10
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