Question

Determine the unbalanced force acting on an iron ball (r=1.5cm, density of iron = 7.8 g/cm^3) when just released while totally immersed in (a) water and (b) mercury (density of mercury = 13.6 g/cm^3). What will be the initial acceleration of the ball in each case?

Answer 1

Unbalanced force = Weight in air - Buoyant force.

Mass = density * volume =

Weight = Mass* g =

A) When the ball is fully submerged, then volume of ball is same as volume of liquid displaced.

Mass of water displaced = density of water * vol of ball.

Volume of iron ball =

Mass of water displaced = 1 * 14.1 = 14.1 g

Weight of water displaced = 0.0141*9.8 = 0.139 N. = Byoyant force (archemedes principle)

Unbalanced force 1.08 - 0.139 = 0.942 N.

Initial accleration = Unbalanced force/mass = 0.942/0.1103 = 8.54 m/s² (downwards)

B) Mass of mercury displaced = 14.1 * 13.6 = 191.76g

Buoyant force = weight of mercury displaced = 0.19176*9.8 = 1.88 N

Unbalanced force = 1.08 - 1.88 = -0.8 N.

-ve sign indicate that the ball will go upward and will not submerge in mercury. (you can also verify it by comparing density of both ball and mercury.)

Initial accleration will be = -0.8/0.1103 = -7.25 m/s² (upwards)

Thank You !!!