The formula E = mc² states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3×10⁸ m/s) squared. Write a program that accepts the mass of an object and determines its energy.

The formula E = mc² states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the

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Q. The formula E = mc² states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3\times10⁸ m/s) squared. Write a program that accepts the mass of an object and determines its energy.

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Concept understanding — Squaring A Number

Squaring a Number – From Intuition to Precision

Think of a square tile on a floor. If the tile has a side of length 2 units, how many small unit squares fit inside it? You'd count 2 rows of 2 squares each — that's $2 \times 2 = 4$ squares. That act of multiplying a number by itself is what we call squaring the number.

The name comes directly from geometry: the area of a square is side $\times$ side. So "2 squared" is the area of a square of side 2. That's why we write it as $2^2$ — the little 2 (the exponent) tells you to use the base (2) as a factor twice.

Note

The small raised number is called the exponent or power. In $5^2$ , the base is 5 and the exponent is 2. It means $5 \times 5$ .

The Precise Statement

For any real number $a$ , the square of $a$ is defined as:

a^2 = a \times a

We read $a^2$ as "a squared" or "a to the power 2". The result is always a real number.

What Happens with Different Types of Numbers?

Type of $a$	Example	$a^2$	Why?
Positive integer	$3$	$3^2 = 9$	$3 \times 3$
Negative integer	$-4$	$(-4)^2 = 16$	$(-4) \times (-4) = 16$ (negative $\times$ negative = positive)
Zero	$0$	$0^2 = 0$	$0 \times 0$
Fraction	$\frac{1}{2}$	$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$	$\frac{1}{2} \times \frac{1}{2}$
Decimal	$0.3$	$0.3^2 = 0.09$	$0.3 \times 0.3$

Watch out

A very common mistake: $(-3)^2$ is not $-9$ . The parentheses matter. $(-3)^2 = (-3) \times (-3) = 9$ . But $-3^2$ means $-(3 \times 3) = -9$ . The exponent only applies to the number directly before it.

Why Does Squaring a Negative Give a Positive?

This is a crucial conceptual point. Multiplication is repeated addition, but with signs it's about direction. Think of a number line. Multiplying by $-1$ flips direction. So $(-3) \times (-3)$ means: start at 0, take 3 steps backward (that's $-3$ ), but do it $-3$ times — which means reverse direction again. Two reversals bring you back to the positive side. The result is $9$ .

Important

The square of any real number is never negative. The smallest possible square is $0^2 = 0$ . Every other square is positive. This is why equations like $x^2 = -4$ have no real solution — no real number, when squared, gives a negative.

The Perfect Squares

Numbers like $1, 4, 9, 16, 25, 36, \dots$ are called perfect squares because they come from squaring an integer. Memorising the first 15–20 perfect squares saves a lot of time in exams.

$n$	$n^2$
1	1
2	4
3	9
4	16
5	25
6	36

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Read the mass, square the speed of light (c = 3 × 10⁸ m/s) and multiply:

mass = float(input("Enter mass of the object in kg: "))
c = 3 * 10**8            # speed of light in m/s
energy = mass * c**2
print("Equivalent energy =", energy, "joules")

Sample run (mass = 5 kg):

Enter mass of the object in kg: 5
Equivalent energy = 4.5e+17 joules
``` …

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energy = mass × c², with c = 3 × 10⁸ m/s written as 3 * 10**8 — a 5 kg mass gives 4.5e+17 joules, printed in scientific notation.

The concept is squaring with the exponent operator and handling very large numbers: Python computes them exactly (ints) or shows them in scientific notation (floats), so no special handling is needed for a number like 9 × 10¹⁶.

# E = m * c**2 : mass-energy equivalence
mass = float(input("Enter mass of the object in kg: "))
c = 3 * 10**8              # speed of light in m/s
energy = mass * c**2
print("Equivalent energy =", energy, "joules")

Key lines:

3 * 10**8 — precedence: ** before *, so this is 3 × 10⁸ = 300000000. (Writing 3e8 is an equivalent float literal.)
c**2 = 9 × 10¹⁶; multiplying by the float mass makes the result a float, which Python prints in scientific notation once it is large.

Sample run (example values):

Enter mass of the object in kg: 5
Equivalent energy = 4.5e+17 joules

Working: c² = (3×10⁸)² = 9×10¹⁶; E = 5 × 9×10¹⁶ = 45×10¹⁶ = 4.5×10¹⁷ J — Python displays this as 4.5e+17. …

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Q.The formula E = mc² states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3×10⁸ m/s) squared. Write a program that accepts the mass of an object and determines its energy.

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