An explosion blows a stationary rock into three parts. Two parts of masses (1 ~kg ) and (2 ~kg ) moves at right angles to one another with velocities (12 ~ms ⁻¹ ) and (8 ~ms ⁻¹ ), respectively. If the velocity of third part is 4 ( ms ⁻¹ ),

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An explosion blows a stationary rock into three parts. Two parts of masses (1 ~kg ) and (2 ~kg ) moves at right angles to one another with velocities (12 ~ms ⁻¹ ) and (8 ~ms ⁻¹ ), respectively. If the velocity of third part is 4 ( ms ⁻¹ ), the mass of the rock is

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Correct answer: A. (8 ~kg )

Given, (m₁=1 ~kg , m₂=2 ~kg ), (v₁=12 ~ms ⁻¹, v₂=8 ~ms ⁻¹ and v₃=4 ~ms ⁻¹ ) Since, in the explosion of stationary rock, the momentum is conserved, so ( aligned p _i & = p _f 0 & = p _f= p ₁+ p ₂+ p ₃ aligned ) where, ( p ₁=m₁ v ₁, p ₂=m₂ v ₂ ) and ( p ₃=m₃ v ₃ ) ( aligned p ₃ & =- ( p ₁+ p ₂ ) p ₃ & = p ₁^2+ p ₂^2+2 p ₁ p ₂ p ₃ & = 12^2+16^2+2 12 16 90^ p ₃ & =20 m₃ v₃ & =m₃ 4=20 m₃=5 ~kg aligned ) Hence, the mass of the rock is, ( aligned & m=m₁+m₂+m₃ & m=1+2+5=8 ~kg aligned ) So, the correct option is (a).

An explosion blows a stationary rock into three parts. Two parts of masses (1 ~kg ) and (2 ~kg ) moves at right angles to one another with velocities (12 ~ms ⁻¹ ) and (8 ~ms ⁻¹ ), respectively. If the velocity of third part is 4 ( ms ⁻¹ ), the mass of the rock is

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