Two cylindrical rods of same meterial have the same temperature difference between their ends. The ratio of rates of flow of heat through them is 1 : 8. The ratio of the radii of the rods are 1 : 2. What is the ratio of their lengths ?

Options

A. `2 : 1`
B. `4 : 1`
C. `1 : 8`
D. `1 : 32`

Answer

A

Explanation

As `H=(delta theta)/( R )`
`rArr``H prop (1)/( R ) prop (kA)/(l)`
`rArr` `(H_(1))/(H_(2)) =(A_(1))/(A_(2)) xx (l_(2)) /(l_(1))`
`rArr``(1)/(8) = (1)/(4) xx(l_(2))/(l_(1))`
`rArr``(l_(1))/(l_(2)) =(8)/(4)=(2)/(1)`