KCET 2021 Physics Solved Paper

Given, m1=1‌kg
u1=12ms−1
m2=2‌kg
u2=−24ms−1
(-ve sign implies that, it is travelling in the opposite direction)
e=

2

3

As we know, coefficient of restitution, e=

v2−v1

u1−u2

.

2

3

=

v2−v1

12+24

2

3

=

v2−v1

36

or v2−v1=24 ...(i)
According to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
⇒ m1u1+m2u2=m1v1+m2v2
Substituting the given values in the above relation, we get
1×12+2×(−24)=1×v1+2v2
⇒ 12−48=v1+2v2
⇒ v1+2v2=−36 ...(ii)
Solving Eqs.(i) and (ii), we get
v2=−4ms−1
⇒ −4−v1=24 [∵ from Eq. (i) ]
⇒ v1=−24−4
=−28ms−1