A shell of mass 100 kg is fired horizontally from a cannon with a mass of `5xx10^(3) kg`. The kinetic energy of the shell at the end of the barrel is `7.5xx10^(6) J`. The kinetic energy imparted to the cannon by the recoil is

Options

A. `2xx10^(5) J`
B. `7.5 xx10^(6) J`
C. `1.5 xx10^(5) J`
D. `10^(5)J`

Answer

C

Explanation

m=100 kg
`M=5xx10^(3) kg`
Initially system is at rest `vec(F)_(ext)=0, vec(V)_(cm)=0, Deltavec(P)=0`
`vec(P)_("shell")=-vec(P)_("Gun") rArr P_("Shell")^(2)=P_("Gun")^(2)`
`K_("Shell")=(P_(S)^(2))/(2m), K_("Cannon")=(P_(C)^(2))/(2M)`
`(K_("Connon"))/(K_("Shell"))=m/M=100/5000=1/50` , `K_("Connon")=K_("Shell")1/50=(7.5xx10^(6))/50=1.5xx10^(5)J`