Answer

Verified

21.6k+ views

**Hint:**We can use conservation of momentum to find the momentum of the fourth fragment and then use conservation of energy to find the total energy of explosion.

**Complete step by step answer:**

Let the mass of each fragment after the explosion be $m$ . Since the mass is the same for all fragments , the kinetic energy gets equally divided between the four fragments.

Thus, ${E_1} = {E_2} = {E_3} = E$

Momentum of each fragment $\left( p \right)$ = $\sqrt {2mE} $

The fourth fragment after explosion will fly off in a direction opposite to the direction of resultant of the other three fragments. This we know by the conservation of momentum, i.e., the total momentum of the system is zero before and after the explosion.

Momentum of fourth fragment is thus ${p_4}$

${p_4} = \sqrt {p_1^2 + p_2^2 + p_3^2} $

\[{p_4} = \sqrt {2mE + 2mE + 2mE} \]

\[{p_4} = \sqrt {6mE} \]

Kinetic energy of the fourth fragment can then be found in the following way:

\[p = mv\] and \[E = \dfrac{1}{2}m{v^2}\]

Solving these two by eliminating \[v\] from both the equations we get

\[{E_4} = \dfrac{{p_4^2}}{{2m}}\]

\[{E_4} = \dfrac{{6mE}}{{2m}}\]

\[{E_4} = 3E\]

Therefore energy of explosion is the sum of energy of the four fragments = \[{E_1} + {E_2} + {E_3} + {E_4}\]

\[ = E + E + E + 3E\]

\[ = 6E\]

**Thus the answer is option $B$ .**

**Note:**The conservation of momentum can be applied here since net external force is zero. Similar is the reason for conserving energy. We also should take care of the calculations since tricky questions like this have huge chances of calculation error.

Recently Updated Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main

Find the points of intersection of the tangents at class 11 maths JEE_Main

For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

Other Pages

The electronic configuration of chloride ion is A 2 class 11 chemistry JEE_Main

When the diameter of the conductor is doubled then class 12 physics JEE_Main

Equipotential at a great distance from a collection class 12 physics JEE_Main

A household uses the following electric appliances class 12 physics JEE_Main

Define 1 Ohm resistance A student has a resistance class 12 physics JEE_Main

A metallic rod PQ of length l is rotated with an angular class 12 physics JEE_Main