A body of mass 2,kg makes an elastic collisio | vedclass

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(B) Let the mass of the first body be $m_1 = 2\,kg$ and its initial velocity be $u_1$. Let the mass of the second body be $m_2$,which is initially at

Vedclass · Accepted Answer

$1.2$

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(B) Let the mass of the first body be $m_1 = 2\,kg$ and its initial velocity be $u_1$. Let the mass of the second body be $m_2$,which is initially at rest $(u_2 = 0)$.For a one-dimensional elastic collision,the final velocity $v_1$ of the first body is given by the formula:$v_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) u_1$Given that the body continues to move in the original direction with one-fourth of its original speed,we have $v_1 = \frac{u_1}{4}$.Equating the two expressions:$\frac{u_1}{4} = \left( \frac{2 - m_2}{2 + m_2} \right) u_1$$\frac{1}{4} = \frac{2 - m_2}{2 + m_2}$$2 + m_2 = 4(2 - m_2)$$2 + m_2 = 8 - 4m_2$$5m_2 = 6$$m_2 = \frac{6}{5} = 1.2\,kg$.Thus,the mass of the second body is $1.2\,kg$.

$A$ body of mass $2\,kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth of its original speed. The mass of the second body which collides with the first body is .......... $kg$.

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