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Heat and Thermodynamics question

2020 · 5 Sep · Shift 1 · Q52
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  5. /2020 · 5 Sep · Shift 1 · Q52

Heat and Thermodynamics question

2020 · 5 Sep · Shift 1 · Q52

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g – oC) (1 cal = 4.2 × 107 ergs) close to :
  1. A
    87.5 oC
  2. B
    83.3 oC
  3. C
    38.4 oC
  4. D
    119.2 oC
View written solutionFree

Correct answer: A

  1. Given data
  • Mass of bullet: m=5 g=0.005 kgm = 5\ \text{g} = 0.005\ \text{kg}m=5 g=0.005 kg
  • Speed of bullet: v=210 m/sv = 210\ \text{m/s}v=210 m/s
  • Specific heat of bullet material: s=0.030 cal/(g∘C)s = 0.030\ \text{cal/(g}^\circ\text{C)}s=0.030 cal/(g∘C)
  • Half of the bullet's kinetic energy is converted into heat in the bullet.
  1. Initial kinetic energy of the bullet
K=12mv2K = \frac{1}{2}mv^2K=21​mv2

Substituting values:

K=12(0.005)(210)2K = \frac{1}{2}(0.005)(210)^2K=21​(0.005)(210)2 K=0.0025×44100=110.25 JK = 0.0025 \times 44100 = 110.25\ \text{J}K=0.0025×44100=110.25 J

So, heat produced in the bullet is half of this:

Q=110.252=55.125 JQ = \frac{110.25}{2} = 55.125\ \text{J}Q=2110.25​=55.125 J
  1. Convert heat into calories

Since 1 cal=4.2 J1\ \text{cal} = 4.2\ \text{J}1 cal=4.2 J,

Q=55.1254.2=13.125 calQ = \frac{55.125}{4.2} = 13.125\ \text{cal}Q=4.255.125​=13.125 cal
  1. Use calorimetry relation
Q=msΔTQ = ms\Delta TQ=msΔT

Here m=5 gm = 5\ \text{g}m=5 g and s=0.030 cal/(g∘C)s = 0.030\ \text{cal/(g}^\circ\text{C)}s=0.030 cal/(g∘C).

Thus,

13.125=5×0.030×ΔT13.125 = 5 \times 0.030 \times \Delta T13.125=5×0.030×ΔT 13.125=0.15ΔT13.125 = 0.15\Delta T13.125=0.15ΔT ΔT=13.1250.15=87.5∘C\Delta T = \frac{13.125}{0.15} = 87.5^\circ \text{C}ΔT=0.1513.125​=87.5∘C
  1. Check options
  • A: 87.5∘87.5^\circ87.5∘C ✅
  • B: 83.3∘83.3^\circ83.3∘C
  • C: 38.4∘38.4^\circ38.4∘C
  • D: 119.2∘119.2^\circ119.2∘C

Therefore, the correct option is A.

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