At what speed v will the mass of an object be 10% greater than its rest mass?
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The mass-energy equivalence relation `E = mc^2` gives the energy released when an object with mass m is completely converted to energy. Alternately, as the energy of an object is increased there is a corresponding increase in its mass.
If an object with rest mass `M_o` moves at v m/s, the mass of the object is increased to `M = M_o/(sqrt(1 - v^2/c^2))` , where c is the speed of light.
Let the mass of an object be 10% greater than the rest mass at speed v,
`1.1*M_o = M_o/(sqrt(1 - v^2/c^2))`
=> `sqrt(1 - v^2/c^2) = 1/1.1`
=> `1 - v^2/c^2 = 1/1.21`
=> `v^2/c^2 = 21/121`
=> `v^2 = (21/121)*c^2`
=> `v = (sqrt(21)/11)*c`
=> `v ~~ 0.4166*c`
The mass of an object is 10% greater than the rest mass when its speed is 0.4166*c
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