A particle of mass 4 m explodes into three pieces of masses m, m and 2 ~m . The equal masses move along X -axis and Y -axis with velocities 4 ~ms ⁻¹ and 6 ~ms ⁻¹ respectively. The magnitude of the velocity of the heavier mass is

Step-by-step solution

Let third mass particle (2 ~m ) moves making angle with X -axis. The horizontal component of velocity of 2 ~m mass particle =u and vertical component =u From conservation of linear momentum in X -direction array rlrl or & m₁ u₁+m₂ u₂ =m₁ v₁+m₂ v₂ or & 0 =m 4+2 m(u ) or & -4 =2 u array Again, applying law of conservation of linear momentum in Y -direction. aligned 0 & =m 6+2 m(u ) - 6 2 & =u aligned or -3=u (ii) Squaring Eqs. (i) and(ii) and adding, we get aligned (4) +(9) & =u^2 ^2 +u^2 ^2 & =u^2 ( ^2 + ^2 ) aligne