Concepts Of Physics MCQ Edition [Volume 1]PhysicsGeometrical Optics
A gun of mass M fires a bullet of mass m with a horizontal speed V . The gun is equipped with a concave mirror of focal length f facing towards the receding bullet. Determine the speed of separation of the bullet and the image immediately after the gun is fired.
Options
- A2 (1 + m M )V
- B(1 + m M )V
- C2V
- D2 (1 - m M )V
Correct answer
A. 2 (1 + m M )V
Step-by-step solution
Let the velocity of the bullet with respect to the ground be V in the forward direction. By the principle of conservation of linear momentum, the recoil velocity of the gun (and the mirror) is: v_ g = m M V (in the backward direction) The velocity of the bullet with respect to the mirror (gun) is: v_ O/M = V - (-v_ g ) = V + m M V = V (1 + m M ) For a spherical mirror, the velocity of the image with respect to the mirror is given by: v _ I/M = -m_ t ^2 v _ O/M where m_ t = f f - u is the transverse magnification. I