A shell of mass 20 kg at rest explodes

Asked by admin @ 17/08/2021 in Physics viewed by 387 People

A shell of mass 20 kg at rest explodes into twofragments whose masses are in the ratio 2 : 3.The smaller fragment moves with a velocity of6 m/s. The kinetic energy of the larger fragment is(1) 96 J(2) 216 J(3) 144J(4) 360 J

Answered by admin @ 17/08/2021

Answer:

Option (1) 96 J

Explanation:

Given in the question :

• Total Mass : 20 Kg

• velocity of smaller fragment : 6m/s

As the shell of mass of 20 kg explodes into 2 fragments in ratio of 2:3 ,Let it be 2x : 3x

→ 2x + 3x = 20

→ 5x = 20

→ x = 4

2*4 = 8 kg 3*4 = 12 kg

Mass of fragments : 8 Kg and 12 Kg

Smaller fragment moves with velocity of 6 m/s i.e 8 kg ones . Let velocity of 12 kg ones be ' v '

Applying Conservation of Linear Momentum

Pi = 20*0 { initially at rest }

Pf = 8*6 - 12*v

-» Pi = Pf

→ 0 = 8*6 - 12v

→ 0 = 48 - 12v

→ 12v = 48

→ v = 4 m/s

Velocity of larger fragment ( 12 kg ones ) is 4 m/s

We have to take out kinetic energy ( KE ) of larger fragment

→ KE = 1/2*12*(4)^2

Kinetic Energy = 96 J

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