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A lead ball of specific heat $125 Jk {g^{- 1}}^{0} C^{- 1}$ at $20^{0} C$ is dropped from a height of 2km. It is subjected to air resistance, and it is assumed that all of its kinetic energy is used in increasing the temperature of ball. Final temperature of the ball in $^{0} C$ is _________ times initial temperature of ball in $^{0} C$ .

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Detailed Solution

$According to Joule's Law W = JH \Rightarrow mgh = Jms (t_{2} - t_{1})$

$△ T = \frac{10 \times 2000}{125} = 160 {}^{o}C$

$T_{f} - 20 = 160 \Rightarrow T_{f} = 180 {}^{o}C$

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