A U-tube has a liquid of density `rho_(0)` at `0^(@) C`. In the two limbs they are kept to a length `l_(1)` and `l_(2)` at a constant temperature of `t_(1)` and `t_(2)` respectively. Then, the cubical expansion coefficient will be

Options

A. `(l_(1)-l_(2))/(l_(2)t_(1)-l_(1)t_(2))`
B. `(l_(1)-l_(2))/(l_(1)t_(1)-l_(2)t_(2))`
C. `(l_(1)+l_(2))/(l_(2)t_(1)+l_(1)t_(2))`
D. `(l_(1)+l_(2))/(l_(1)t_(1)+l_(2)t_(2))`

Answer

A

Explanation

Pressure at the bottom In both arms will be equal `((rho_(0))/(1+gammat_(1)))l_(1) = ((rho_(0))/(1+gammat_(2)))l_(2) = implies gamma = (l_(1) - l_(2))/(l_(2)t_(1) - l_(1)t_(2))`