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Arrive at Einstein's mass-energy relation by dimensional method (E = mc^(2)). |
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Answer» Solution :Let us assume that the Energy E depends on mass m and velocity of light c. `E prop m^(a)c^(B)` `E = km^(a)c^(b)` where k is a constant Dimensions of E = `[ML^(2)T^(-2)]` Dimensions of m = [M] Dimensions of c = `[LT^(-1)]` Substituting the values in the above EQUATION `[ML^(2)T^(-2)] = K[M]^(a)[LT^(-1)]^(b)` By EQUATING the dimensions a = 1 , b = 2 -b = -2 `E = k.mc^(2)` The value of constant k = 1 `E = mc^(2)`. This is Einstein.s mass energy relation. |
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