A body of mass ( 5 ± 0 . 5 ) kg is moving with a velocity of ( 20 ±...

The kinetic energy is given by,

$K = \dfrac{1}{2}m{v}^{2}$

Differentiating the above equation,

$dK = \dfrac{1}{2} ( {v}^{2}dm + 2mvdv )$

Dividing by $K$,

$⇒ \dfrac{dK}{K} = \dfrac{dm}{m} + \dfrac{2dv}{v}$

$⇒ \dfrac{dK}{1000} = \dfrac{0 . 5}{5} + \dfrac{2 \times 0 . 4}{20}$

$⇒ dK = 100 + 40 = 140$

$⇒ KE = ( 1000 \pm 140 ) J$