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Answer :
The volume of the rock is 0.186 m^3.
The initial acceleration of the rock is given as 0.4 g downwards. To find the volume of the rock, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
First, let's convert the acceleration to m/s^2. We know that 1 g = 9.8 m/s^2, so 0.4 g = 0.4 * 9.8 m/s^2 = 3.92 m/s^2.
Next, we need to calculate the weight of the rock. The weight of an object is given by the formula: weight = mass * acceleration due to gravity. In this case, the mass of the rock is 185 kg and the acceleration due to gravity is 9.8 m/s^2. Therefore, the weight of the rock is 185 kg * 9.8 m/s^2 = 1813 N.
Since the initial acceleration of the rock is downward, the buoyant force acting on it is equal to the weight of the rock. Therefore, the buoyant force is 1813 N.
Now, let's use the formula for the buoyant force: buoyant force = density of fluid * volume * acceleration due to gravity. Since the rock is under water, the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2. Rearranging the formula, we can solve for the volume of the rock: volume = buoyant force / (density of fluid * acceleration due to gravity). Plugging in the values, we get: volume = 1813 N / (1000 kg/m^3 * 9.8 m/s^2) = 0.186 m^3.
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