A body of dimensions 1.5 m x1.0 m x 2 m, weighs 1,962 N in water. Find its weight inair. What will be its specific gravity?

To solve this problem, we need to follow these steps:

Step 1: Calculate the volume of the body. The volume (V) of a rectangular body is given by the formula V = length x width x height. So, the volume of the body is 1.5 m x 1.0 m x 2 m = 3 cubic meters.

Step 2: Calculate the buoyant force. The buoyant force (Fb) is the weight of the fluid displaced by the body. Since the body weighs 1,962 N in water, the buoyant force is 1,962 N.

Step 3: Calculate the weight of the body in air. The weight of the body in air (Wa) is the buoyant force plus the weight of the body in water. So, Wa = Fb + weight in water = 1,962 N + 1,962 N = 3,924 N.

Step 4: Calculate the density of the body. The density (ρ) of the body is its mass divided by its volume. Since weight is mass times gravity, we can find the mass by dividing the weight in air by the acceleration due to gravity (9.8 m/s^2). So, the density of the body is ρ = Wa / (V x g) = 3,924 N / (3 m^3 x 9.8 m/s^2) = 133.6 kg/m^3.

Step 5: Calculate the specific gravity. The specific gravity (SG) of a substance is the ratio of its density to the density of water (1,000 kg/m^3). So, the specific gravity of the body is SG = ρ / ρ_water = 133.6 kg/m^3 / 1,000 kg/m^3 = 0.1336.

So, the weight of the body in air is 3,924 N and its specific gravity is 0.1336.