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A blast breaks a body initially at rest of mass 0.5 kg into 3 pieces,2 smaller pieces of equal mass and the third double the mass of either of a small piece.After the blast the two smaller masses move at right angles to one another with equal speed.Find the statements that is/are true for this case asuming that the energy of blast is totally transferred to masses.(A) All the three pieces share the energy of blast equally(B)The speed of bigger mass is √(2) times the speed of either of the smaller mass.(C)The direction of motion of bigger mas makes an angle of 135 with the direction of smaller pieces (D)The bigger piece carries double the energy of either piece

Navneet Kumar , 6 Years ago
Grade 12
anser 1 Answers
Agrata Singh

Last Activity: 6 Years ago

i and j represent the  unit vectors in positive X and Y dirxn respectively in the solution below
Let the masses be m1 mmsuch that m1=m2=0.5/4=m and m3=0.5/2=2m
Let velocity of m1 be v1=v i ,of m2 be v2=v j of mbe v3
Conservation of linear momentum gives
0=m1v1+m2v2+m3v3
0=mv i + mv j + 2mv3
v3=-1/2(v i + v j)
|v3|=1/2v (√2)=v/√2
 
Now writing energies of the particles 
E1=E2=1/2mv2
E3=1/2x2mx(v3)2= ½ mv2 
Hence E1=E2=E3
 
Regarding the third option v3 does make an angle of 135 with the smaller mass velocities. You can see that from the vector relationship 
 
Hence the correct answer is (A)(C)

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