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

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

Question

(C) In an elastic collision,the total kinetic energy is conserved. However,the question asks for the loss in kinetic energy of the colliding body. Let

Vedclass · Accepted Answer

$4/9 \ mv^2$

Vedclass · Answer

(C) In an elastic collision,the total kinetic energy is conserved. However,the question asks for the loss in kinetic energy of the colliding body. Let the mass of the first body be $m_1 = m$ and its initial velocity be $u_1 = v$. Let the mass of the second body be $m_2 = 2m$ and its initial velocity be $u_2 = 0$.After the collision,the final velocity $v_1$ of the first body is given by the formula: $v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1 + \frac{2m_2}{m_1 + m_2} u_2$.Substituting the values: $v_1 = \frac{m - 2m}{m + 2m} v + 0 = \frac{-m}{3m} v = -v/3$.The initial kinetic energy of the first body is $K_i = 1/2 \ mv^2$.The final kinetic energy of the first body is $K_f = 1/2 \ m(v_1)^2 = 1/2 \ m(-v/3)^2 = 1/2 \ m(v^2/9) = 1/18 \ mv^2$.The loss in kinetic energy of the colliding body is $\Delta K = K_i - K_f = 1/2 \ mv^2 - 1/18 \ mv^2$.$\Delta K = (9/18 - 1/18) \ mv^2 = 8/18 \ mv^2 = 4/9 \ mv^2$.

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. What is the loss in kinetic energy of the colliding body?

Similar Questions

$A$ ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $m/s$.

$A$ particle of mass $m$ with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass $3m$ at rest. It moves with a velocity $v\hat{j}$ after collision. Then, $v$ is given by:

Discuss elastic collision in two dimensions.

$A$ block having mass $m$ collides with another stationary block having mass $2m$. The lighter block comes to rest after the collision. If the initial velocity of the first block is $v$,then the value of the coefficient of restitution must be:

An object of mass $M_1$ moving horizontally with speed $u$ collides elastically with another object of mass $M_2$ at rest. Select the correct statement.

Vedclass Test Series

Exam Paper Generator

Online Exam Module