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A massless spring (K=800 N/m), attached ...

A massless spring (K=800 N/m), attached with a mass (500g) is completely immersed in 1 kg of water. The springs is stretched by 2cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibratioins 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^(-1)k`

B

`10^(-4)k`

C

`10^(-3)k`

D

`10^(-5)k`

Text Solution

Verified by Experts

The correct Answer is:
D
Potential Energy of spring =Total Head Energy `1/2kA^(2)=m_(1)s_(1)Deltatheta+m_(2)s_(2)Deltatheta`
`Deltatheta=(1/2KA^(2))/(m_(1)s_(1)+m_(2)s_(2))` `Deltatheta=(400xx(2/100)^(2))/(4184+200)=3.6xx10^(-15)k`
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