An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 ~kg first part moving with a velocity of 12 ~ms ⁻¹ and 2 ~kg second part moving with a velocity of 8 ~ms ⁻¹ . If the third part flies off with a velocity of 4 ~ms ⁻¹ , its mass would be

Step-by-step solution

Key Idea Apply law of conservation of linear momentum. Momentum of first part =1 12=12 ~kg ~ms ⁻¹ Momentum of the second part =2 8=16 ~kg ~ms ⁻¹ Resultant momentum = (12)^2+(16)^2 =20 ~kg ~ms ⁻¹ The third part should also have the same momentum. Let the mass of the third part be, then aligned 4 M & =20 M & =5 ~kg aligned Alternative : aligned Mv & =12 Mv & =16 & = 16 12 = 4 3 M & = 12 5 4 3 = 60 12 =5 ~kg aligned