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Check the following equation by dimensional analysis 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 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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