Question

A body falling from a height of $10m$ rebounds from hard floor. If it loses $20$ energy in the impact, then coefficient of restitution is .....

• A. $0.89$
• B. $0.56$
• C. $0.23$
• D. $0.18$

Answer 1

The correct option is A $0.89$

KE just before the collision will be $loss$ in $PE$ so $K_i=mgh=m\times 10\times 10=100m$

loss due to impact was $20$ % so $remaining$ KE will be $K_f=100m\times 80$% or $K_f=100m\times 0.8=80m$

Now the velocity of strike will be $V_i=\sqrt{\frac{2K_i}{m}}=10\sqrt{2}m/s$

and the velocity after rebound will be $V_f=\sqrt{\frac{2K_f}{m}}=4\sqrt{10}m/s$

coeefificient of restitution will be $e=\frac{V_f}{V_i}=\frac{4\sqrt{10}}{10\sqrt{2}}=0.89$