Question

An object hooked up to a dynamometer in the air shows 2.35 n when immersed in water, the dynamometer reads 1.65 n, given the known gravity of water, 10 n/m³. How many cubic centimeters is the volume of the object?

Answer 1

To find the volume of the object, we can use the buoyancy formula:

Buoyancy force = density of fluid * volume of object * gravitational acceleration

In this case, the buoyancy force is the difference between the reading on the dynamometer when the object is in the air (2.35 n) and when it is in water (1.65 n), or 0.7 n. We can rearrange the buoyancy formula to solve for volume:

Volume of object = buoyancy force / (density of fluid * gravitational acceleration)

Plugging in the values, we get:

Volume of object = 0.7 n / (10 n/m³ * 9.8 m/s²)

Solving for volume, we get:

Volume of object = 0.0072 m³

This is the volume of the object in cubic meters. To find the volume in cubic centimetres, we can convert the volume to cubic centimeters by multiplying by 1,000,000:

Volume of object in cubic centimeters = 0.0072 m³ * 1,000,000 cm³/m³

This simplifies to:

Volume of object in cubic centimeters = 72 cm³

So the volume of the object is 72 cubic centimeters.