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A lead ball at 25^@C is dropped from a h...

A lead ball at `25^@`C is dropped from a height of 2 km. It is heated due to air resistance and it is assumed that all of its kinetic energy is used in increasing the temperature of ball. Find the final temperature of the ball.

A

`283.73^@C`

B

`353.73^@C`

C

`463.73^@C`

D

`183.73^@C`

Text Solution

Verified by Experts

The correct Answer is:
D
If there is no air resistence, velocity of ball, on reaching ground is
`V=sqrt(2gh)=sqrt(2xx10xx2000)=200(m)/(s)`
Kinetic energy of ball is `k=(1)/(2)mv^2`
`=(1)/(2)xxmxx(200)^2=2xx10^4xxmJ`
If all the kinetic energy is absorbed by the ball it gets heated.
Due to this, temperature of ball is increased by `DeltaT`, we have
`k=msDeltaT`
or `2xx10^4xxm=mxx126xxDeltaT`
or `DeltaT=(2xx10^4)/(126)=158.73^@C`
`:. T_f=25+158.73=183.73^@C`
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Knowledge Check

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