Work Energy And Power Question 116
Question: A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is [EAMCET 2001]
Options:
A) $ h( \frac{1+e^{2}}{1-e^{2}} ) $
B) $ h( \frac{1-e^{2}}{1+e^{2}} ) $
C) $ \frac{h}{2}( \frac{1-e^{2}}{1+e^{2}} ) $
D) $ \frac{h}{2}( \frac{1+e^{2}}{1-e^{2}} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
Particle falls from height h then formula for height covered by it in nth rebound is given by $ h _{n}=he^{2n} $
where e = coefficient of restitution,
n = No. of rebound Total distance travelled by particle before rebounding has stopped $ H=h+2h_1+2h_2+2h_3+2h _{n}+…….. $
$ =h+2he^{2}+2he^{4}+2he^{6}+2he^{8}+……… $
$ =h+2h(e^{2}+e^{4}+e^{6}+e^{8}+…….) $
$ =h+2h[ \frac{e^{2}}{1-e^{2}} ]=h[ 1+\frac{2e^{2}}{1-e^{2}} ]=h( \frac{1+e^{2}}{1-e^{2}} ) $
