Question

If two perfectly elastic balls of masses 2 gm and 3 gm moving in opposite directions with speeds of 8 m/s and 6 m/s respectively collide elastically, their final velocities are respectively.

• A. $5.2m{s}^{-1},8.8m{s}^{-1}$
• B. $8.8m{s}^{-1},5.2m{s}^{-1}$
• C. $-8.8m{s}^{-1},-5.2m{s}^{-1}$
• D. $-8.8m{s}^{-1},5.2m{s}^{-1}$

Answer 1

Answer: (D)

$-8.8m{s}^{-1},5.2m{s}^{-1}$

Momentum conservation
$2\times 8-6\times 3=2v_1+3v_2$
$-2=2v_1+3v_2$

$e=\frac{v_2-v_1}{8-(-6)}=1$

$v_2-v_1=14$
$\Rightarrow v_1=-8.8$ m/s
$v_2=5.2$ m/s.