A body of mass 5 kg makes an elastic collisi | vedclass

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Question

(A) Let the mass of the first body be $m_1 = 5 \ kg$ and its initial velocity be $u$. Let the mass of the second body be $M$ and its initial velocity

Vedclass · Accepted Answer

$4.09$

Vedclass · Answer

(A) Let the mass of the first body be $m_1 = 5 \ kg$ and its initial velocity be $u$. Let the mass of the second body be $M$ and its initial velocity be $u_2 = 0$.After the elastic collision,the first body moves with velocity $v_1 = \frac{u}{10}$ in the same direction. Let the velocity of the second body be $v_2$.By the law of conservation of linear momentum:$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$5u + M(0) = 5 \left(\frac{u}{10}ight) + M v_2$$5u = \frac{u}{2} + M v_2 \implies M v_2 = 4.5u$  --- $(i)$For an elastic collision,the coefficient of restitution $e = 1$,so:$v_2 - v_1 = e(u_1 - u_2)$$v_2 - \frac{u}{10} = 1(u - 0)$$v_2 = u + \frac{u}{10} = \frac{11u}{10}$ --- (ii)Substituting $v_2$ from (ii) into $(i)$:$M \left(\frac{11u}{10}ight) = 4.5u$$M = \frac{4.5 	imes 10}{11} = \frac{45}{11} \approx 4.09 \ kg$.

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after the collision with a velocity equal to $\frac{1}{10}$th of its original velocity. Then the mass of the second body is (in $kg$)

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