Consider two hot bodies `B_(1)` and `B_(2)` which have temperature `100^(@)"C"` and `80^(@)"C"` respectively at t = 0. The temperature of surroundings is `40^(@)" C"`. The ratio of the respective rates of cooling `R_(1)` and `R_(2)` of these two bodies at` t = 0` will be

Options

A. `R_(1) : R_(2) = 3 : 2`
B. `R_(1) : R_(2) = 5 : 4`
C. `R_(1) : R_(2) = 2 : 3`
D. `R_(1) : R_(2) = 4 : 5`

Answer

A

Explanation

From Newton's law of cooling,
`R = (dT)/(dt) prop (T-T_(0))`
`rArr(R_(1))/(R_(2)) =(100-40)/(80-40) =(60)/(40) =(3)/(2)`
`rArr`` R_(1) : R_(2) = 3 : 2`