A block of mass `0.50 kg` is moving with a speed of `2.00 cm^(-1)` can a smooth surface . It strikes another mass of `1.00 kg ` and then they move togather as a single body . The energy less charing the collision is

Options

A. `0.16 J`
B. `1.00 J`
C. `0.67 J`
D. `0.34 J`

Answer

C

Explanation

(c ) Initial kinetic energy of the system
`K.E, = (1)/(2) mu^(2) + (1)/(2) M(0)^(2) = (1)/(2) xx 0.5 xx 2 xx 2 + 0 = 1J`
For collision , uppying conservation of linear momentum
`m xx u = (m+ M) xx nu `
`:. 0.5 xx 2 = (0.5 +1) xx nu rArr nu = (2)/(3) m//s `
Final kinetic energy of the system is
`K.E_(f) = (1)/(2) (m+M) nu^(2) = (1)/(2) (0.5 + 1) xx(2)/(3) xx (2)/(3) = (1)/(3) j`
:. Energy loss during collision `= (1 - (1)/(3)) J = 0.67 J`