Question

A bomb of mass 15 kg initially at rest explodes into two pieces 5 kg and 10 kg. If the kinetic energy of the 5 kg mass is 250 J, then the velocity of 10 kg mass is: Options 1 4 m/s 2 5 m/s 3 8 m/s 4 10 m/s

Answer 1

kinetic energy of the first one is given show the velocity would be same of both of them so we will first find the velocity of first one.

1/2mv^2=250
1/2*5*v^2=250
v^2=100
v=10

so if the bomb explode the velocity of both of the particles would be seen so my answer is 10 M per second

Answer 2

Given,

Initial mass= 15kg

Final masses= 5 kg and 10 kg

The kinetic energy of 5 kg mass= 250J

To find,

The velocity of the 10 kg mass

Solution,

We can solve this numerical problem by using the following process.

When the bomb of 15 kg explodes, it breaks into two pieces of 5kg and 10 kg. The kinetic energy of the 5kg mass is 250J.

We know that,

∴ Kinetic energy = $\frac{1}{2} mv^2$

            250 J  = $\frac{1}{2} * 5* v^2$

                     v₁ = $\sqrt{\frac{250*2}{5} }$

                     v₁  = 10 m/s

Thus, the velocity of the 5kg ball is 10 m/s.

Now,

By the conservation of the momentum;

 ∴   mv = m₁ v₁ + m₂ v₂

⇒ 15×0 = 5*10 + 10* v₂

⇒      v₂ = -5 m/s

Thus, the velocity of the 10kg ball is 5 m/s. (Option B)

(This will be considered as the final result. As the initial units are in the SI system, we have to use the SI unit for the final answer also. And, the SI unit of velocity is m/s.)