Check if the answer is 2.76 cm, not 2.76 mm. I'm rather sure it
is 2.76 cm.
Soln:
U can draw a U tube, left side with oil and water, right side with
water
let the height of water at the left side = x cm
thus the height of water at the right side = 30 - x cm
Also, height of oil at the left side = 12 cm
Using pgh,
pressure at the bottom due on left side = 12 (920) + x (1000)
pressure at the bottom due on right side = (30 - x) (1000)
Equating both sides of the pressure, x = 9.48 cm
Repeat the above for heigh of oil = 12 + 6 = 18cm
you will get a new x of 6.72 cm
Hence, the difference = 2.76 cm => the water level rose by 2.76
cm on the other side.
--------------------------------------------------------------------------------------------
Alternatively, you can use this method if you understand the
concept
when 6 cm of oil is added onto one side, the extra pressure will
have to be balanced out; i.e. the pressure on the left side (oil
side) will have to decrease by 3cm of oil, whereas the pressure on
the right side will have to increase by 3cm of oil.
height of water level that is equal to pressure due to 3cm of
oil
= (3 * 10 * 920) / (10 * 1000)
= 2.76 cm