2) An accelerometer can be made from a liquid-filled U-tube as shown. The air pressure at the open end is the same on both limbs of the manometer. Derive an expression for the acceleration a, in terms of liquid level difference, tube geometry, and fluid density (). Hint: First relate the pressure at the bottom of each limb to the pressure at the top of that limb (which is clearly equal to Patm ) - for this you will have to apply the vertical component of the force balance equation for fluid undergoing rigid body motion; then relate the pressure at the bottom of the one limb to the pressure at the bottom of the second limb - for this you will have to apply the horizontal component of the force balance equation for fluid undergoing rigid body motion; combine these equations to find the desired