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 10 m/s and 30 m/s respectively, strike each other and stick together. [2026]

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Solution

Q.
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 10 m/s and 30 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 $31 cal/kg ° C$ and 1 cal = 4.2 J) [2026]

1 1.95

2 1.15

3 1.75

4 1.44

Ans.
(4)

${(K . E .)}_{lost} = \frac{1}{2} μ V_{rel}^{2} (1 - e^{2})$

$= \frac{1}{2} (\frac{m_{1} m_{2}}{m_{1} + m_{2}}) {(10 + 30)}^{2} (1 - 0)$

$= \frac{1}{2} [\frac{(15) (25)}{40}] {[40]}^{2}$

$= 7500 J$

${(K . E .)}_{loss} = (m_{1} + m_{2}) (S) (Δ T)$

$[S = 31 \times 4.2 J/kg- ° C]$

$7500 = (40) (31) (Δ T)$

$Δ T = \frac{7500}{40 \times 31 \times 4.2} = 1.44 ° C$

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