A metallic ball of mass 100 g and specific heat capacity 2 J `kg^(-1)K^(-1)` was dropped from a height of 6 m on to a perfectly non-conducting surface. If 80% of its kinetic energy is converted into heat on striking the surface, find the change in temperature of the ball. (Take g=1000 cm `s^(-2)`).

Explanation

The length of Fahrenheit and centigrade thermometers is =20 cm
When temperature raises from `0^(@)C" to "4^(@)C`, then the length of mercury thread in Celsius scale of temperature is `=(20xx4)/(100)=0.8` cm.
In Fahrenheit thermometer, `0^(@)C` is represented by `32^(@)F` and the number of divisions in it is 180.
`(C)/(5)=(F-32)/(9)rArrF=(9)/(5)C+32`
When temperature in Celsius scale is `4^(@)C`, then its corresponding temperature in Fahrenheit scale is
`F=(9)/(5)C+32`
`F=(9)/(5)xx4+32=(196)/(5)=39.2^(@)F`
The rise in temperature in Fahrenheit scale
`=39.2^(@)F-32^(@)F=7.2^(@)F`
When temperature raises from `32^(@)F" to "39.2^(@)F`, then the increase in the length of mercury level is
`rArr" "(7.20xx20)/(180)=0.8` cm
Then the ratio of the length of mercury threads in centigrade and Fahrenheit temperature scales is
`=(0.8)/(0.8)=(1)/(1)=1:1`