Question
In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg , moving in opposite directions with speeds of $10\text{ }m/s$ and $30\text{ }m/s$, respectively, strike each other and stick together. The rise in temperature (in $\ ^{\circ}C$ ), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material $31cal/kg.\ ^{\circ}C$ and $1cal = 4.2\text{ }J$ )
Options
Solution
$(K.E)_{\text{lost~}} = \frac{1}{2}\mu{\text{ }V}_{\text{rel~}}^{2}\left( 1 - e^{2} \right)$
$$\begin{matrix} & \ = \frac{1}{2}\left( \frac{{\text{ }m}_{1}{\text{ }m}_{2}}{{\text{ }m}_{1} + m_{2}} \right)(10 + 30)^{2}(1 - 0) \\ & \ = \frac{1}{2}\left\lbrack \frac{(15)(25)}{40} \right\rbrack\lbrack 40\rbrack^{2} \\ & \ = 7500\text{ }J \\ & \ (\text{ }K.E)_{\text{loss~}} = \left( m_{1} + m_{2} \right)(S)(\Delta T) \\ & \left\lbrack S = 31 \times 4.2\text{ }J/kg - \ ^{\circ}C \right\rbrack \\ & 7500 = (40)(31)(\Delta T) \\ & \Delta T = \frac{7500}{40 \times 31 \times 4.2} = {1.44}^{\circ}C \end{matrix}$$
Create a free account to view solution
View Solution Free