A body of mass 8kg at rest ecplodes into three parts whose masses are in the ratio 1:3:4. The bigger parts travel with a velocity 10m/s in perpendicular directions after the explosion. Velocity of the third part is
Answers
Answer: Total mass of the body M=1 kg
So, mass of first fragment m
1
=
5
1
×1=0.2 kg
Mass of second fragment m
2
=
5
1
×1=0.2 kg
Mass of third fragment m
3
=
5
3
×1=0.6 kg
Velocity of masses m
1
and m
2
, v=30 m/s
Momentum of first fragment p
1
=m
1
v=0.2×30=6 kg m/s
Similarly, p
2
=m
2
v=0.2×30=6 kg m/s
Third fragment will fly in a direction opposite to the direction of resultant of p
1
and p
2
so that total momentum of the system after explosion remains zero.
Momentum of the third fragment p
3
=
p
1
2
+p
2
2
∴ p
3
=
6
2
+6
2
=6
2
kg m/s
Thus speed of third fragment v
3
=
m
3
p
3
=
0.6
6
2
=10
2
m/s
⟹ x=2