Consider an elastic collision of a particle o | vedclass

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

Question

(B) For an elastic collision between two particles of equal mass $(m_1 = m_2 = m)$, where one particle is initially at rest $(u_2 = 0)$: By conservati

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(B) For an elastic collision between two particles of equal mass $(m_1 = m_2 = m)$, where one particle is initially at rest $(u_2 = 0)$: By conservation of linear momentum: $\vec{p}_1 = \vec{p}_1' + \vec{p}_2'$. Squaring both sides: $p_1^2 = p_1'^2 + p_2'^2 + 2\vec{p}_1' \cdot \vec{p}_2'$. By conservation of kinetic energy: $\frac{1}{2}mu^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2$, which implies $p_1^2 = p_1'^2 + p_2'^2$. Comparing the two equations, we get $2\vec{p}_1' \cdot \vec{p}_2' = 0$. Since the momenta are non-zero, the dot product is zero only if the angle between the final velocity vectors is $90^\circ$. Thus, $	heta_1 + 	heta_2 = 90^\circ$.

Similar Questions

$A$ steel ball of radius $2 \, cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \, cm$ moving at a velocity of $81 \, cm/s$ collides elastically with the first ball. After the collision,the smaller ball moves with a speed of ............. $cm/s$.

Ball $A$ moving at $12 \ m/s$ collides elastically with ball $B$ (initially at rest) as shown in the figure. If both balls have the same mass, what is the final velocity of ball $A$ in $m/s$?

An object of mass $m_{1}$ collides with another object of mass $m_{2}$,which is at rest. After the collision,the objects move with equal speeds in opposite directions. The ratio of the masses $m_{2} : m_{1}$ is

$A$ ball of mass $2 \,kg$ collides with another ball of mass $M$ at rest. If the collision is elastic and after the collision, the first ball moves with $\frac{1}{3}$ of its initial velocity in the same direction, then the mass of the second ball is: (in $\,kg$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module