The velocities of two steel balls before impact are shown. If after head-on impact the velocity of ball B is observed to be 3ms- 1 to the right, the coefficient of restitution is

Question

The velocities of two steel balls before impact are shown. If after head-on impact the velocity of ball B is observed to be 3ms- 1 to the right, the coefficient of restitution is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-cvu19frbwfsujmf8.jpg" /> (A) (7/18) (B) (6/7) (C) (5/18) (D) None of these

Tardigrade Admin · Accepted Answer

By conservation of linear momentum (0 . 6)(4)+(0 . 4)(- 2)=(0 . 6)(vA)+(0 . 4)(3) ⇒ vA=(2/3) Therefore, e=(vs e p e r a t i o n/va p p r o a c h)=(3 - vA/4 + 2)=(7/18)

Q. The velocities of two steel balls before impact are shown. If after head-on impact the velocity of ball $B$ is observed to be $3 m s^{- 1}$ to the right, the coefficient of restitution is

$\frac{7}{18}$

$\frac{6}{7}$

$\frac{5}{18}$

None of these

By conservation of linear momentum
$(0.6) (4) + (0.4) (- 2) = (0.6) (v_{A}) + (0.4) (3)$
$\Rightarrow v_{A} = \frac{2}{3}$
Therefore, $e = \frac{v _{se p er a t i o n}}{v _{a pp ro a c h}} = \frac{3 - v _{A}}{4 + 2} = \frac{7}{18}$

Q. The velocities of two steel balls before impact are shown. If after head-on impact the velocity of ball B is observed to be 3ms−1 to the right, the coefficient of restitution is

187​

76​

185​