Question

A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is $50$m where m is the mass of the one shell. If the muzzle velocity of shell is $200$ m/s, what is recoil speed of car after second shot?

• A. $\frac{200}{49}$ m/s
• B. $200(\frac{1}{48}+\frac{1}{48})$ m/s
• C. $200(\frac{1}{48}+\frac{1}{49})$ m/s
• D. $200(\frac{1}{48}+\frac{1}{48\times 49})$ m/s

Answer 1

The correct option is A $\frac{200}{49}$ m/s

Centre of mass of velocity of shell = 0 (initially at rest)

Therefore,$0=49m\times v+m\times 200$

$v=\frac{-200}{49}m/s$

$\frac{200}{49}m/s$

Another shell is fire , then the velocity of the car , with respect to platform is

$v^{\prime }=\frac{200}{49}ms$ toward left

Another shell is fired , then the velocity of the car with respect to platform is

$v^{\prime }=\frac{200}{48}ms$ towards left