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A massless spring (k = 800 N/m), attache...

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)

A

`10^(-6)K`

B

`10^(-3)K`

C

`10^(-1)K`

D

`10^(-5)K`

Text Solution

Verified by Experts

The correct Answer is:
D
`1/2 KA^2 = m_1s_1 Delta T+m_2s_2 Delta T`
`1/2 xx 800 xx ((2)/(100))^2=1/2xx 400 xx Delta T +4184 xx DeltaT`
`Delta T=(400xx ((2)/(100))^2)/(200+4184)=3.64 xx 10^(-5)K`
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