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JEE Main 2021 (27 Jul, Shift 1) · Elastic Potential Energy

Elastic Potential Energy question from JEE Main 2021 (27 Jul, Shift 1)

Q7JEE Main 2021 · 27 JUL · SHIFT 1Medium

Elastic Potential Energy

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10−6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s. (Young's modulus of rubber = 0.5 ×\times 109 N/m2)

Numerical answer type. Work it out, then open the answer.

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Answer: 20

  1. Elastic energy becomes kinetic energy: YAx22L=12mv2\dfrac{YAx^2}{2L} = \dfrac{1}{2}mv^2.
  2. v2=YAx2mL=0.5×109×10−6×(0.04)20.02×0.1=0.80.002=400v^2 = \dfrac{YAx^2}{mL} = \dfrac{0.5 \times 10^9 \times 10^{-6} \times (0.04)^2}{0.02 \times 0.1} = \dfrac{0.8}{0.002} = 400
  3. v=20 m/sv = 20\text{ m/s}
  4. So the answer is 20 m/s.
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