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Question: A shell of mass 200 g is fired by a gun of mass 100 kg. If the muzzle speed of the shell is \(80 \ma...

A shell of mass 200 g is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s−180 \mathrm {~m} \mathrm {~s} ^ { - 1 }, then the recoil speed of the gun is :

A

16 cm s−116 \mathrm {~cm} \mathrm {~s} ^ { - 1 }

B

8 cm s−18 \mathrm {~cm} \mathrm {~s} ^ { - 1 }

C

8 m s−18 \mathrm {~m} \mathrm {~s} ^ { - 1 }

D

16 m s−116 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Answer

16 cm s−116 \mathrm {~cm} \mathrm {~s} ^ { - 1 }

Explanation

Solution

Here

Mass of the shell

Mass of gun, M = 100 g

Muzzle speed of the shell

Recoil speed of the gun

According to the principle of conservation of linear

=−16×10−2 ms−1=−16cms−1= - 16 \times 10 ^ { - 2 } \mathrm {~ms} ^ { - 1 } = - 16 \mathrm { cms } ^ { - 1 }

-ve sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell.