A sphere of mass 2 kg moving at 36 km/hr collides head on with another sphere of mass 3 kg kept at rest . If after collision both spheres moves together then kinetic energy decreases by collision will be `……….`

Options

A. 40 J
B. 60 J
C. 100 J
D. 140 J

Answer

B

Explanation

Momentum is conserved in collision
` :. M_(1)v_(1) =m_(2)v_(2)=(m_(1)+m_(2))V`
Where V = combine velocity of spheres
` 2xx 10 +3 + 3 xx 0 = (2 + 3)V`
` :. 5V = 20`
` :. V = 4` m/s
Initial kinetic of system `K_(1)=1/2 m_(1)v_(1)^(2) [ :. v_(2) = 0 ] `
` = 1/2 xx2xx100`
` = 100 J `
Final kinetic energy `K_(2) =1/2 (m_(1)+m_(2))V^(2)`
`=1/2 (2+3)(4)^(2)`
` =(5xx16)/2`
= 40 J
` :. ` Kinetic energy decreases = `100 J - 40 J `
= 60 J