A 400 kg. wooden log is floating with 0.2 of its volume above water level. Given that the density of iron is 7.8 gram per centimeter cubic, calculate the least mass of iron object attached to the underside of log that will sink it.

To find the least mass of the iron object that will sink the wooden log, we need to consider the buoyancy force acting on the log.

First, let's calculate the volume of the wooden log that is above the water level. We know that 0.2 of the log's volume is above water level, so we can determine the total volume by dividing this value by 0.8:

Volume of log = (0.2 / 0.8) * Volume of log
= 0.25 * Volume of log

Next, let's calculate the weight of the wooden log acting downwards. The weight of an object can be calculated using the formula:

Weight = Mass * Acceleration due to gravity

Given that the mass is 400 kg and the acceleration due to gravity is 9.8 m/s^2:

Weight of log = 400 kg * 9.8 m/s^2
= 3920 N (Newtons)

Now, let's calculate the buoyant force acting on the wooden log. The buoyant force is equal to the weight of the fluid the log displaces, which in this case is water. As the log is floating, the buoyant force is equal to the weight of the log:

Buoyant force = Weight of log
= 3920 N

To sink the log, the total downward force exerted on it (including the weight of the log and the mass of the iron object) must be greater than the buoyant force. Therefore, the least mass of the iron object that will sink the wooden log can be calculated as:

Mass of iron object = (Buoyant force - Weight of log) / Acceleration due to gravity
= (3920 N - 3920 N) / 9.8 m/s^2
= 0 kg

The least mass of the iron object required to sink the wooden log is 0 kg. This means that any amount of iron added to the log will cause it to sink.