A pendulum bob weighs 80 N in air. When immersed in water, it weighs 70 N. When immersed in liquid Y, it weighs 65 N. What is the relative density of liquid Y?

Alright — let's do this. This problem involves Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The "displaced" force mentioned in the question refers to this buoyant force. Step 1: Identify the buoyant forces. When the pendulum bob is totally immersed in water, the buoyant force (F_B, water) is equal to the weight of the water displaced. F_B, water = 10 N When the pendulum bob is totally immersed in liquid Y, the buoyant force (F_B, Y) is equal to the weight of liquid Y displaced. F_B, Y = 15 N Step 2: Relate buoyant force to density and volume. The buoyant force is given by the formula F_B = _fluid V_displaced g, where _fluid is the density of the fluid, V_displaced is the volume of the fluid displaced, and g is the acceleration due to gravity. Since the bob is totally immersed, the volume of fluid displaced is equal to the volume of the bob (V_bob). So, for water: F_B, water = _water V_bob g = 10 N (1) And for liquid Y: F_B, Y = _Y V_bob g = 15 N (2) Step 3: Calculate the relative density of liquid Y. The relative density (or specific gravity) of liquid Y is defined as the ratio of its density to the density of water: Relative Density of Y = (_Y)/(_water) To find this ratio, we can divide equation (2) by equation (1): F_B, YF_B, water = _Y V_bob g_water V_bob g The terms V_bob and g cancel out, leaving: F_B, YF_B, water = (_Y)/(_water) Substitute the given buoyant forces: Relative Density of Y = 15 N10 N Relative Density of Y = 1.5 The final answer is B) 1.50. Send me the next one 📸