If a body collides inelastically with another | vedclass

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

Question

(B) Let $u_1$ be the initial speed of the first body and $u_2 = 0$ be the initial speed of the second body.Let $v_1$ and $v_2$ be their respective spe

Vedclass · Accepted Answer

$\frac{1-e}{1+e}$

Vedclass · Answer

(B) Let $u_1$ be the initial speed of the first body and $u_2 = 0$ be the initial speed of the second body.Let $v_1$ and $v_2$ be their respective speeds after the collision.By the law of conservation of linear momentum: $m u_1 + m(0) = m v_1 + m v_2$,which simplifies to $u_1 = v_1 + v_2$.The coefficient of restitution $e$ is defined as $e = \frac{v_2 - v_1}{u_1 - u_2} = \frac{v_2 - v_1}{u_1}$.Substituting $u_1 = v_1 + v_2$ into the equation for $e$: $e = \frac{v_2 - v_1}{v_1 + v_2}$.Rearranging the terms: $e(v_1 + v_2) = v_2 - v_1 \implies ev_1 + ev_2 = v_2 - v_1$.Grouping $v_1$ and $v_2$ terms: $v_1(1 + e) = v_2(1 - e)$.Therefore,the ratio of their speeds is $\frac{v_1}{v_2} = \frac{1 - e}{1 + e}$.

If a body collides inelastically with another body of the same mass initially at rest,what will be the ratio of their speeds after the collision?

Similar Questions

$A$ ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to the same height,then the coefficient of restitution $e$ is $[g = 10\, m/s^2]$.

$A$ ball is dropped from a height $h$. It bounces repeatedly off the ground. What is the total distance covered by the ball before it comes to rest?

$A$ ball of mass $m$ strikes a smooth ground at an angle $\alpha$ as shown in the figure and is deflected at an angle $\beta$. The coefficient of restitution will be

$A$ ball with a speed of $9\, m/s$ collides with another identical ball at rest. After the collision,the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $x : y$ where $x$ is........

$A$ sphere of mass $m$ moving with velocity $u$ collides with another sphere of the same mass $m$ at rest. If the coefficient of restitution is $e = \frac{1}{2}$, what is the ratio of their velocities after the collision?

Vedclass Test Series

Exam Paper Generator

Online Exam Module