Q.

A loaded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation θ.The gun is initially at rest on a horizontal friction less surface. After firing  the centre of mass of the gun-shot system

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a

Moves with a velocity mvM

b

Moves with a velocity mvMcosθ in the horizontal direction

c

Moves with a  velocity mvsinθM+m along vertical direction

d

Moves with a velocity vM-mM+m  in horizontal direction

answer is C.

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Detailed Solution

as there is no force acting in the horizontal direction velocity of the center of mass remain zero but vertical direction bullet has a velocity vsinθ;so velocity of center of mass along vertical direction is   mvsinθM+m
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A loaded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation θ.The gun is initially at rest on a horizontal friction less surface. After firing  the centre of mass of the gun-shot system