A body of mass `1 kg`, initially at rest, explodes and breaks into three fragments of masses in the ratio `1:1:3`. The two pieces of equal mass fly off perpendicular to each other with a speed of `30 m//s` each. What is the velocity of the heavier fragment?

Options

A. `10sqrt2ms^(-1)`
B. `5sqrt3ms^(-1)`
C. `10sqrt3ms^(-1)`
D. `5sqrt2ms^(-1)`

Answer

D

Explanation

Conservation of momentum during explosion yields
`impliesvecP_(1)+vecP_(2)+vecP_(3)=0impliesvecP_(3)=|vecP_(1)+vecP_(2)|`
`implies m_(3)vecv_(3)=|m_(1)vecv_(1)+m_(2)vecv_(2)|`
since `vecv_(1)_|_vecv_(2)impliesvecv_(3)=sqrt((m_(1)^(2)v_(1)^(2)+m_(2)^(2)v_(2)^(2))/(m_(3)))`
`implies vecv_(3)=sqrt(((m_(1))/(m_(3)))^(2)+v_(1)^(2)+((m_(2))/(m_(3)))^(2)v_(2)^(2))`
`impliessqrt((1/3)^(2)(15)^(2)+(1/3)^(2)(15)^(2))` (`:'m_(1),m_(2):m_(3)=1:1:3`)
`impliesv_(3)=5sqrt(2)ms^(-1)`