Q15 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Work Power Energy

A massless platform is kept on a light elastic spring, as shown in the figure. When particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle sticks to the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m?

Figure

  • A
    0.96 m
  • B
    2.96 m
  • Correct answer
    C
    3.96 m
  • D
    0.48 m

Solution

Let the particle be dropped from a height h and the spring be compressed by y. According to conservation of mechanical energy,
Loss in potential energy of the particle = gain in elastic potential energy of the spring

∴ mg h⁡ + y = 1 2 k y 2

Now, as the particle and spring remain same, hence

h⁡ 1 + y 1 h⁡ 2 + y 2 = y 1 y 2 2

0 · 2 4 + 0 · 0 1 h⁡ 2 + 0 · 0 4 = 0 · 0 1 0 · 0 4 2

Solving we get, h2 = 3.96 m

Hence, the correct answer is option: 'C'.

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