At what speed the volume of an object shrinks to half its rest value ?

Explanation

Let the volume (initial ) be 'V'
` V' = V/ 2 `
So, `V / 2 = V (sqrt 1 - v^(2) /c^(2))`
`c / 2 = (sqrt c^(2) - v^(2))`
`c^(2) / 4 = c ^(-2)- v^(2)`
`rArr c^(2) / 4 = c^(2) -v^(2) `
v^(2) = c^(2) - c^(2) / 4 - = 3 / 4 c^(2)`
v = (sqrt 3 ) / 2 c`.