A stationary body breaks into four identical fragments. Three fly mutually perpendicular with kinetic energy E₀ each. If total energy released is nE₀, find n.
Physics · Mixed Chapter
JEE Main Practice

Question

A stationary body breaks into four identical fragments. Three fly mutually perpendicular with kinetic energy E₀ each. If total energy released is nE₀, find n.

G1 Physics · Accepted Answer

Step 1: Each of first three fragments has equal momentum magnitude p, because masses and energies are equal. Step 2: The three momentum vectors are orthogonal, so resultant magnitude is √(p²+p²+p²)=p√3. Step 3: Fourth fragment must have opposite momentum of magnitude p√3. With same fragment mass, its kinetic energy is 3E₀. Step 4: Total kinetic energy released =3E₀+3E₀=6E₀; n=6.