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

$A$ light particle moving horizontally with a speed $v_1$ strikes a very heavy block moving in the same direction with a speed $v_2$. The collision is elastic. After the collision,the velocity of the particle is:

$A$ sphere of mass $0.1\,kg$ is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension,this sphere hits a block of the same mass at rest on a frictionless table. If the impact is elastic,then the kinetic energy of the block after the collision is ............. $J$.

$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body due to the collision is ............ $m/s$.

Assertion $(A)$: In an elastic collision between two bodies,the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason $(R)$: In an elastic collision,the linear momentum of the system is conserved.

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.