1. Tardigrade
  2. Question
  3. Physics
  4. A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

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Q. A massless spring ($k = 800 \,N/m$), attached with a mass ($500\, g$) is completely immersed in $1\, kg$ of water. The spring is stretched by $2\, cm$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = $400\, J/kg\, K$, specific heat of water = $4184\, J/kg\, K)$

JEE MainJEE Main 2019Thermal Properties of Matter

Solution:

By law of conservation of energy
$\frac{1}{2} kx^2 = (m_1s_1+ m_2 s_2) \Delta T$
$\Delta T = \frac{16 \times 10^{-2}}{4384} = 3.65 \times 10^{-5}$ .