A steel ball of radius 2 ,cm is at rest on a | vedclass

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(A) Let the radius of the first ball be $r_1 = 2 \,cm$ and the second ball be $r_2 = 4 \,cm$.Assuming both balls are made of the same material with de

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$144 \,cm \,s^{-1}$

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(A) Let the radius of the first ball be $r_1 = 2 \,cm$ and the second ball be $r_2 = 4 \,cm$.Assuming both balls are made of the same material with density $ho$, the mass $m$ is given by $m = \frac{4}{3} \pi r^3 ho$.Thus, the ratio of masses is $\frac{m_1}{m_2} = \frac{r_1^3}{r_2^3} = \left(\frac{2}{4}ight)^3 = \frac{1}{8}$, which implies $m_2 = 8m_1$.For a one-dimensional elastic collision, the final velocity $v_1$ of the first ball (initially at rest) is given by the formula:$v_1 = \left(\frac{2m_2}{m_1 + m_2}ight) u_2$, where $u_2 = 81 \,cm \,s^{-1}$ is the initial velocity of the second ball.Substituting the values:$v_1 = \left(\frac{2(8m_1)}{m_1 + 8m_1}ight) 	imes 81$$v_1 = \left(\frac{16m_1}{9m_1}ight) 	imes 81$$v_1 = \frac{16}{9} 	imes 81 = 16 	imes 9 = 144 \,cm \,s^{-1}$.

$A$ steel ball of radius $2 \,cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \,cm$ moving with velocity of $81 \,cm \,s^{-1}$ collides elastically with the ball which is at rest. After collision, the ball with radius of $2 \,cm$ moves with a speed of:

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