A stationary shell explodes into two fragments having masses in the ratio 1:2. The heavier fragment attains a kinetic energy of 100 J. Find the kinetic energy released in the explosion (J).
Physics · Mixed Chapter
JEE Main Practice

Question

A stationary shell explodes into two fragments having masses in the ratio 1:2. The heavier fragment attains a kinetic energy of 100 J. Find the kinetic energy released in the explosion (J).

G1 Physics · Accepted Answer

Step 1: Before explosion, total momentum is zero, so the fragments have equal and opposite momenta of magnitude p. Step 2: Let lighter fragment mass = m and heavier = 2m. Step 3: Their kinetic energies are Kₗ = p²/(2m) and Kₕ = p²/(4m). Therefore Kₗ/Kₕ = 2. Step 4: Given Kₕ = 100 J, Kₗ = 200 J. Step 5: Total kinetic energy released = 100 + 200 = 300 J. Final answer: 300 J.