Question bank/JEE Main/Physics

JEE MainPhysicsModerateCentre of Mass

A railway flat car has an artillery gun installed on it and
contains shells for fring The combined system excluding shell has a mass
M and moves with a velocity v0v_{0}. The barrel of the gun makes an
angle α\alpha with the horizontal. A shell of mass m leaves the barrel
at a speed relative to initial state of barrel in the forward
direction. The speed of the flat car so that it may stop after the
firing is: (neglect frinstion)

Show answer and solution
u - velocity of shell with respect to gun.
In horizontal direction F→ext=0{\overset{\rightarrow}{F}}_{ext} = 0, so
centre of mass move with constant velocity in horizontal plane.
(M+m)v0=m(v0+ucosα)(M + m)v_{0} = m(v_{0} + ucos\alpha)
V0=mucosαMV_{0} = \frac{mucos\alpha}{M}

Source: Grass-G / P-07 Physics paper 17 October.docx

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