Question

# A gun fires a shell and recoils horizontally. if the shell travels along the barrel with speed v, the ratio of speeds with which the gun recoils, if the barrel is (i) horizontal (ii) inclined at an angle of 30∘ with horizontal, is

A
1
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B
23
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C
34
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D
12
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Solution

## The correct option is B 2√3Let velocity of the shell is v and mass is m and velocity of the gun is v1 in case of horizontally fired and v2 when inclined with horizontal and mass is M. Case 1: When fired horizontally ∴ mv=Mv1 ∴ v1=mvM ...(i) Case 2: When inclined with horizontal mvcos 30∘=Mv2 ∴ v2=√3mv2M ...(ii) From equation (i) and (ii) we get, v1v2=2√3 ∴(b) .

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