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A shell moving with a velocity of 500 m/...

A shell moving with a velocity of 500 m/s, suddenly explodes into two pieces of masses `m_(1)` and `m_(2)`. They continue to move with velocities of 600 m/s and 200 m/s in the same direction. What is the ratio `(m_(1))/(m_(2))` of the two pieces?

A

`2:1`

B

`1:1`

C

`3:1`

D

`4:1`

Text Solution

Verified by Experts

The correct Answer is:
C
Original momentum of the shell = 0 as it is rest.

Linear momentum of `A ( P_(A)) = 1 xx 12 = 12 `
Linear momentum of `B ( P_(B)) = 2 xx 16 = 32 `
`:.` Resultant momentum of A and B
`P' = sqrt(12^(2)+32^(2)) = sqrt( 144 + 1024) = sqrt( 1168)`
`:. P' = 34.2 kg m//s`
Linear momentum of C` = m xx 40 kg m//s `
`:.` Total momentum of A,B and C `= ( 34.2 + 40 m ) `
`:.` By the principle of conservation of linear momentum, `34.2+40m=0`
`:. m = ( 34.2 )/(40) = 0.85 kg`
( Mass cannot be negative sign is neglected. )
Thus mass of the shell `= 1+ 2 + 0.85 =3.85 kg`
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