A body of mass m at rest gets exploded into 3 parts, having masses in the ratio 1: 1:3. Its two parts having equal masses move at right angles to each other with 15 m/s each. The velocity of third is:

Options

A. `5sqrt2 ms^(-1)`
B. `5 ms^(-1)`
C. `10sqrt2 ms^(-1)`
D. `sqrt2 ms^(-1)`

Answer

a

Explanation

The mass of three parts are `m/5.m/5` and `(3m)/(5)`.The resultant of momnets of two parts flying at right angle to each other must be equal and opposite to momnetum of third part.

Now `p_(12)=sqrt(p_(1)^(2)+p_(2)^(2))=p_(1)sqrt2=m/5xx15sqrt2`
Also `p_(3)=(3m)/(5)xxv`
`:. (3m)/(5)v=(15m)/(5)xxsqrt2`
`implies v+(15)/(3)xxsqrt2` or `v=5sqrt2 ms^(-1)`