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A 30 kg shell moving in free space explodes into three fragments of equal masses. After explosion, the fragments move apart under influence of their mutual forces of interactions. At some instant of time after the explosion, velocities of the fragments relative to an inertial frame are (3î + 2ĵ)m/s, –2î m/s and (5î – 5ĵ)m/s. If whole of the energy released in the explosion is converted into kinetic energy of the three fragments, how much energy has been released in the explosion? (1) 260 J (2) 290 J (3) 335 J (4) 410 J

A 30 kg shell moving in free space explodes into three fragments of equal masses. After explosion, the fragments move apart under influence of their mutual forces of interactions. At some instant of time after the explosion, velocities of the fragments relative to an inertial frame are (3î + 2ĵ)m/s, –2î m/s and (5î – 5ĵ)m/s.
 
If whole of the energy released in the explosion is converted into kinetic energy of the three fragments, how much energy has been released in the explosion?
(1) 260 J
(2) 290 J
(3) 335 J
(4) 410 J

Grade:12

1 Answers

Parth Kohli
24 Points
9 years ago
It should be clear that the 30 kg shell breaks into three shells with mass 10 kg each. Since it is given that the energy released in the explosion is converted into kinetic energy of the three masses, we can simply calculate the kinetic energy of each and add them to get the energy released.
 
E = KE1 + KE2 + KE3 
= ½ m (v12 + v22 + v32 ) = ½ * 10 * (13 + 4 + 50) = ½ * 10 * (67) = 335 J.

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