Numerical Problem No. 1.9 (Measurements) Physics HSSC - I (Class -11); Physics (Punjab Curriculum and Text Board, Lahore) With Verified Answers

Show that the famous "Einstein equation" E = mc² is dimensionally consistent.

 

Given:

E = mc²
where 

E = Energy

m = mass

c = velocity of light 

To Find:

To show that the equation E = mc² is dimensionally consistent

Solution:

As given 

E = mc²

Dimensions of L.H.S. of the equation = [E] = [ML²T⁻²]

Dimensions of R.H.S. of the equation = [m] + [c]²

                                                        = [M] + [LT⁻¹]²

                                                        = [ML²T⁻²]

L.H.S = R.H.S

Hence proved that the equation E = mc² is dimensionally consistent.

Similar Question:

Show that the expression of vf =vi +at is dimensionally correct, where vi is the velocity at t = 0 , a is acceleration and vf is the velocity at time t. 

Verify that the given equation S = vᵢt + `\frac {1}{2}` at² is dimensionally correct.

 The speed v of sound waves through a medium may be assumed to depend on (a) the density 𝝆 of the medium and (b) its modulus of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions, the formula for the speed of sound.

What are the dimensions and units of gravitational constant G in the formula 

F = G`\frac {m₁m₂}{r^2}`

Show that (a) KE = `\frac {1}{2}` mv² and  (b) PE𝖌 = mgh are dimensionally correct. 

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Numerical Problem 1.9
⇑

List of 11th Physics Numerical Problems of Chapter - 1

⇑

Numerical Problem 1.8  ⇚   11th Physics Main Content List    ⇛ Numerical Problem 1.10

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