A body of mass m moving with velocity v colli | vedclass

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

Question

(D) The velocity of the first body after a one-dimensional elastic collision is given by the formula:$v_{1} = \left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\ri

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) The velocity of the first body after a one-dimensional elastic collision is given by the formula:$v_{1} = \left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1} + \frac{2 m_{2} u_{2}}{m_{1}+m_{2}}$Given $m_{1} = m$,$m_{2} = 2m$,$u_{1} = v$,and $u_{2} = 0$:$v_{1} = \left(\frac{m - 2m}{m + 2m}\right) v + \frac{2(2m)(0)}{3m} = \left(\frac{-m}{3m}\right) v = -\frac{v}{3}$Initial kinetic energy of the first body: $KE_{i} = \frac{1}{2} mv^{2}$Final kinetic energy of the first body: $KE_{f} = \frac{1}{2} m\left(-\frac{v}{3}\right)^{2} = \frac{1}{2} m \left(\frac{v^{2}}{9}\right) = \frac{KE_{i}}{9}$The ratio of $KE_{i}$ to $KE_{f}$ is:$\frac{KE_{i}}{KE_{f}} = \frac{KE_{i}}{KE_{i}/9} = 9$Thus,the ratio is $9 : 1$.

$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. The ratio of the $K.E.$ of the colliding body before and after the collision will be: (in $: 1$)

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:

$A$ body of mass $m$ is at rest. Another body of the same mass moving with velocity $V$ makes a head-on elastic collision with the first body. After the collision,the first body starts to move with velocity:

$A$ moving body with mass $m_1$ strikes a stationary mass $m_2$. What should be the ratio $\frac{m_1}{m_2}$ so as to decrease the velocity of the first body by $1.5$ times after the collision?

$A$ particle of mass $m$ collides with a heavy mass $M$ (initially at rest) elastically. After the collision, the particle returns with $4/9$ of its initial kinetic energy. The mass of the heavy object $M$ is ............... $m$.

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$ at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body $A$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module