A simple accelerometer (an instrument for measuring acceleration) can be made in the form of a tube filled with a liquid and bent as shown. During motion, the level of the liquid in the left arm will be at a height `h_(1)` and in the right arm at a height `h_(2)`. Determine the acceleration a of a carriage in which the accelerometer is installed, assuming that the diameter of the tube is much smaller than `h_(1)` and `h_(2)`.

Options

A. `g(h_(2)+h_(1))/(h_(2)-h_(1))`
B. `g(h_(2)h_(1))/(h_(2)+h_(1))`
C. `g(h_(2)-h_(1))/(h_(2)+h_(1))`
D. `g(h_(2)h_(1))/(h_(2)-h_(1))`

Answer

C

Explanation

`tanphi=a/g=(h_(2)-h_(1))/(h_(2)+h_(1))implies a=(g(h_(2)-h_(1)))/(h_(2)+h_(1))`