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An object of mass 5 kg and speed 10 ms-1 explodes into two pieces of equal mass. One piece comes to rest. The kinetic energy added to the system during the explosion is-
- a)Zero
- b)50 J
- c)250 J
- d)500 J
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
An object of mass 5 kg and speed 10 ms-1explodes into two pieces of eq...
ATQ: Given value mass of object = 5 kg and v = 10 m/s
K.E = 1/2 mv2
1/2 × 5 × 100 = 250 J
K.E = 1/2 mv2
1/2 × 5 × 100 = 250 J
Most Upvoted Answer
An object of mass 5 kg and speed 10 ms-1explodes into two pieces of eq...
According to question , given value object of mass = 5 kg and v = 10 m/s^-1 . K.E = 1/2 mv^2 ;; 1/2 × 5 × 100 = 250 j
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Community Answer
An object of mass 5 kg and speed 10 ms-1explodes into two pieces of eq...
The kinetic energy added to the system during the explosion can be calculated by considering the conservation of momentum and the conservation of kinetic energy.
Conservation of Momentum:
Before the explosion, the object is moving with a speed of 10 m/s. Let's assume the two pieces into which it explodes have equal masses of m kg each. According to the conservation of momentum, the total momentum before the explosion should be equal to the total momentum after the explosion.
Initial momentum = mass × velocity
Initial momentum = 5 kg × 10 m/s = 50 kg·m/s
After the explosion, one piece comes to rest, so the momentum of that piece is zero. The other piece will have the same momentum as the initial momentum because they have equal masses.
Final momentum = 50 kg·m/s
Therefore, the momentum of the second piece after the explosion is also 50 kg·m/s.
Conservation of Kinetic Energy:
The kinetic energy of an object is given by the formula KE = 0.5 × mass × velocity^2.
Before the explosion, the initial kinetic energy of the object can be calculated as follows:
Initial kinetic energy = 0.5 × 5 kg × (10 m/s)^2
Initial kinetic energy = 0.5 × 5 kg × 100 m^2/s^2
Initial kinetic energy = 250 J
After the explosion, one piece comes to rest, so its kinetic energy is zero. The other piece will have the same kinetic energy as the initial kinetic energy because they have equal masses.
Final kinetic energy = 250 J
Therefore, the kinetic energy added to the system during the explosion is 250 J, which corresponds to option C.
Conservation of Momentum:
Before the explosion, the object is moving with a speed of 10 m/s. Let's assume the two pieces into which it explodes have equal masses of m kg each. According to the conservation of momentum, the total momentum before the explosion should be equal to the total momentum after the explosion.
Initial momentum = mass × velocity
Initial momentum = 5 kg × 10 m/s = 50 kg·m/s
After the explosion, one piece comes to rest, so the momentum of that piece is zero. The other piece will have the same momentum as the initial momentum because they have equal masses.
Final momentum = 50 kg·m/s
Therefore, the momentum of the second piece after the explosion is also 50 kg·m/s.
Conservation of Kinetic Energy:
The kinetic energy of an object is given by the formula KE = 0.5 × mass × velocity^2.
Before the explosion, the initial kinetic energy of the object can be calculated as follows:
Initial kinetic energy = 0.5 × 5 kg × (10 m/s)^2
Initial kinetic energy = 0.5 × 5 kg × 100 m^2/s^2
Initial kinetic energy = 250 J
After the explosion, one piece comes to rest, so its kinetic energy is zero. The other piece will have the same kinetic energy as the initial kinetic energy because they have equal masses.
Final kinetic energy = 250 J
Therefore, the kinetic energy added to the system during the explosion is 250 J, which corresponds to option C.
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An object of mass 5 kg and speed 10 ms-1explodes into two pieces of equal mass. One piece comes to rest. The kinetic energy added to the system during the explosion is-a)Zerob)50 Jc)250 Jd)500 JCorrect answer is option 'C'. Can you explain this answer?
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