The correct option is D 16 cms−1
Here,
Mass of the shell, m = 200g = 200×10−3kg
Mass of the gun, M = 100 kg
Muzzle speed of the shell, V = 80 ms−1
Recoil speed of the gun, v = ?
According to the principle of conversation of linear momentum,
mV+Mv=0
v=−mVM=−(200×10−3kg)(80ms−1)100kg
=−16×10−2ms−1=−16cms−1
-ve sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell.