A particle of mass m having collided a stationary particle of mass M = 5m deviates by an angle π/2, whereas the particle of mass M recoiled at angle θ = 30° to the direction of the initial motion of the particle m. The percentage change in kinetic energy of this system after collision is 8 × x%. The value of x is ...
Physics · Mixed Chapter
JEE Mains

Question

A particle of mass m having collided a stationary particle of mass M = 5m deviates by an angle π/2, whereas the particle of mass M recoiled at angle θ = 30° to the direction of the initial motion of the particle m. The percentage change in kinetic energy of this system after collision is 8 × x%. The value of x is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Choose initial motion along +x. After collision m moves perpendicular to +x, while 5m recoils at 30° to the x-axis. Conservation of x-momentum gives mu=5mV cos30°, hence V=2u/(5√3). Step 2: Conservation of y-momentum gives mv₁=5mV sin30°, so v₁=u/√3. Step 3: Final to initial kinetic-energy ratio is [mv₁²+5mV²]/(mu²)=(1/3)+(4/15)=3/5. Step 4: Energy decreases by (1−3/5)×100=40%. Since this equals 8x%, x=5.