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JEE Main 20205 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2020 · 5 September · Morning Shift · Physics · Kinetic Theory of Gases

A bullet of mass 5gram , travelling with a speed of 210m s ^ - 1...

A bullet of mass 5gram5gram, travelling with a speed of 210ms−1210m{s}^{- 1} strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030( gram °C)0 . 030{\left(\text{ gram } ° C\right)}^{- 1}(1calorie=4.2×107ergs)\left(1calorie = 4 .2 \times {10}^{7}ergs\right) close to :

Options

  1. A87.5°C87 . 5 ° C
  2. B83.3°C83 . 3 ° C
  3. C119.2°C119 . 2 ° C
  4. D38.4°C38 . 4 ° C

Correct answer

A. 87.5°C87 . 5 ° C

Step-by-step solution

As per given condition Half of kinetic energy is transferred into heat energy and raises the temperature of bullet

12×12mv2=ms\DeltaT\dfrac{1}{2} \times \dfrac{1}{2}m{v}^{2} = ms\DeltaT

\Deltat=V24s\Deltat = \dfrac{{V}^{2}}{4s}

=210×2104×4.2×0.3×1000=87.5°C= \dfrac{210 \times 210}{4 \times 4 . 2 \times 0 . 3 \times 1000} = 87 . 5 ° C

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