Work Energy And Power Question 318
Question: The ratio of masses of two balls is 2 : 1 and before collision the ratio of their velocities is 1 : 2 in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If e = (5/6), the ratio of speed of each ball before and after collision would be
Options:
A) (5/6) times
B) Equal
C) Not related
D) Double for the first ball and half for the second ball
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let masses of the two ball are 2 m and m and their speeds are u and 2u, respectively.
By conservation of momentum,
$ m_1{{\vec{u}}_1}+m_2{{\vec{u}}_2}=m_1{{\vec{v}}_1}+m_2{{\vec{v}}_2} $
$ \Rightarrow 2mu-2mu=mv_2-2mv_1\Rightarrow v_2=2v_1 $
Coefficient of restitution
$ =-\frac{(v_2-v_1)}{(u_2-u_1)}=-\frac{(2v_1+v_1)}{(-2u-u)}=\frac{-3v_1}{-3u}=\frac{-3v_1}{-3u}=\frac{v_1}{u}=\frac{5}{6} $ [as given]
$ \Rightarrow \frac{v_1}{u_1}=\frac{5}{6}= $ ratio of the speed of first ball before and after collision.
Similarly, we can calculate the ratio of second ball before and after collision,
$ \frac{v_2}{u_2}=\frac{2v_1}{2u}=\frac{v_1}{u}=\frac{5}{6} $
