1 kg body explodes into three fragments. The ratio of their masses is 1 : 1 : 3. The fragments of same mass move perpendicular to each other with speeds 30 m/s, while the heavier part remains in the intial direction. The speed of heavier part is :
m/s
m/s
m/s
m/s
Text Solution
Verified by ExpertsB
Equate the momenta of the system along two perpendicular axes.
Let u be the velocity and θ the direction of the third piece as shown.
Equating the momenta of the system along OA and OB to zero, we get
m × 30 – 3m × v cos θ = 0 .......(i)
and m × 30 – 3m × v sin θ = 0 .......(ii)
These give 3mv cos θ = 3 mv sin θ
or cos θ = sin θ
∴ θ = 45º
Thus, ∠ AOC = ∠ BOC = 180º – 45º = 135º
Putting the value of θ in Eq. (i) we get
30 m = 3mv cos 45º = 
∴ v = 10 
m/s
The third piece will go with a velocity of 10 
m/s in a direction making an angle of 135º with either piece.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems