(D) The fractional loss of kinetic energy $\frac{\Delta K}{K}$ for a particle of mass $m_1$ colliding elastically with a stationary particle of mass $

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(D) The fractional loss of kinetic energy $\frac{\Delta K}{K}$ for a particle of mass $m_1$ colliding elastically with a stationary particle of mass $m_2$ is given by the formula: $\frac{\Delta K}{K} = \frac{4 m_1 m_2}{(m_1 + m_2)^2}$.For a neutron $(m_1 = m)$ colliding with deuterium $(m_2 = 2m)$:$P_d = \frac{4(m)(2m)}{(m + 2m)^2} = \frac{8m^2}{(3m)^2} = \frac{8}{9} \approx 0.89$.For a neutron $(m_1 = m)$ colliding with a carbon nucleus $(m_2 = 12m)$:$P_c = \frac{4(m)(12m)}{(m + 12m)^2} = \frac{48m^2}{(13m)^2} = \frac{48}{169} \approx 0.28$.Thus,the values are $P_d = 0.89$ and $P_c = 0.28$.

Class 11 Physics Work, Energy and Power Elastic Collision

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It is found that if a neutron suffers an elastic collinear collision with deuterium at rest,the fractional loss of its energy is $P_d$; while for its similar collision with a carbon nucleus at rest,the fractional loss of energy is $P_c$. The values of $P_d$ and $P_c$ are respectively:

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A
$(0.28, 0.89)$
B
$(0, 0)$
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$(0, 1)$
D
$(0.89, 0.28)$

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$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.

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Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic,which of the following figure is a possible result after collision?

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Two masses $m_{a}$ and $m_{b}$ moving with velocities $v_{a}$ and $v_{b}$ in opposite directions collide elastically. After the collision,$m_{a}$ and $m_{b}$ move with velocities $v_{b}$ and $v_{a}$ respectively. The ratio $m_{a} : m_{b}$ is:

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$A$ steel ball of radius $2 \, cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \, cm$ moving at a velocity of $81 \, cm/s$ collides elastically with the first ball. After the collision,the smaller ball moves with a speed of ............. $cm/s$.

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$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?

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It is found that if a neutron suffers an elastic collinear collision with deuterium at rest,the fractional loss of its energy is $P_d$; while for its similar collision with a carbon nucleus at rest,the fractional loss of energy is $P_c$. The values of $P_d$ and $P_c$ are respectively:

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$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).$Reason$ : Energy spent against friction does not follow the law of conservation of energy.

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic,which of the following figure is a possible result after collision?

Two masses $m_{a}$ and $m_{b}$ moving with velocities $v_{a}$ and $v_{b}$ in opposite directions collide elastically. After the collision,$m_{a}$ and $m_{b}$ move with velocities $v_{b}$ and $v_{a}$ respectively. The ratio $m_{a} : m_{b}$ is:

$A$ steel ball of radius $2 \, cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \, cm$ moving at a velocity of $81 \, cm/s$ collides elastically with the first ball. After the collision,the smaller ball moves with a speed of ............. $cm/s$.

$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?

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$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.