STATEMENT-1: In an elastic collision between | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In an elastic collision, both linear momentum and kinetic energy are conserved.Let two bodies of masses $m_1$ and $m_2$ have initial velocities $u

Vedclass · Accepted Answer

$Statement-1$ is True, $Statement-2$ is True; $Statement-2$ is $NOT$ a correct explanation for $Statement-1$.

Vedclass · Answer

(B) In an elastic collision, both linear momentum and kinetic energy are conserved.Let two bodies of masses $m_1$ and $m_2$ have initial velocities $u_1$ and $u_2$, and final velocities $v_1$ and $v_2$.Conservation of linear momentum: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$  => $m_1(u_1 - v_1) = m_2(v_2 - u_2)$  (Equation $1$).Conservation of kinetic energy: $\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$ => $m_1(u_1^2 - v_1^2) = m_2(v_2^2 - u_2^2)$  (Equation $2$).Dividing Equation $2$ by Equation $1$: $u_1 + v_1 = v_2 + u_2$ => $u_1 - u_2 = v_2 - v_1$.This shows that the relative velocity of approach $(u_1 - u_2)$ equals the relative velocity of separation $(v_2 - v_1)$. Thus, $Statement-1$ is true.$Statement-2$ is also true because linear momentum is always conserved in any collision (elastic or inelastic) in the absence of external forces. However, the conservation of momentum alone is not sufficient to derive the relative speed property; the conservation of kinetic energy is required. Therefore, $Statement-2$ is not the correct explanation for $Statement-1$.

$STATEMENT-1$: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Because
$STATEMENT-2$: In an elastic collision, the linear momentum of the system is conserved.

Similar Questions

When two identical masses,one of which is at rest,undergo an oblique elastic collision,what is the angle between the two bodies after the collision (in $^{\circ}$)?

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. If their masses are $m_A$ and $m_B$ respectively,then:

Two balls of mass $5 \ kg$ are moving in opposite directions with the same speed of $5 \ m/s$. They undergo a head-on elastic collision. Find the final velocity of the balls in $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$STATEMENT-1$: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Because$STATEMENT-2$: In an elastic collision, the linear momentum of the system is conserved.