A railway carriage of mass 9000 kg moving with a speed of `36kmh^(-1)` collides with a stationary carriage of same mass. After the collision, the carriages get coupled and move together. What is their common speed after collision? What type of collision is this?

Explanation

Mass of moving carriage
`m_(1)=9000kg`
Mass of stationary carriage
`m_(2)=9000kg`
Initial velocity of stationary carriage
`u_(2)=0`
Initial velocity of moving carriage
`u_(1)=36kmh^(-1)`
`=(36xx5)/(18)`
`=10m//s`
Let the common velocity be
`v_(1)=v_(2)=v`
By conservation of momentum
`m_(1)u_(1)+m_(2)u_(2)=(m_(1)+m_(2))v`
`9000xx10+0=(9000+9000)v`
`18000v=90,000`
`v=(90,000)/(18,000)=5ms^(-1)`
`therefore` Common speed `v=5ms^(-1)`
Total K.E before collision
`=(1)/(2)(m_(1)+m_(2))v^(2)`
`=(1)/(2)(9000+9000)xx(5)^(2)`
`=(1)/(2)xx18000xx25`
`=225000J`
`therefore` Total K.E after collision `lt` Total K.E before collision
Hence collision is inelastic.