A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of material can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m³? A)0.50 × 10³ kg B)1.5 × 10³ kg C)2.5 × 10³ kg D)3.5 × 10³ kg

Question

Quizplus · Accepted Answer

The buoyant force acting on the box is given by:
buoyant force = weight of water displaced
Since the box is fully submerged, the buoyant force is equal to the weight of the box and the material loaded onto it. The weight of the box is given by:
weight of box = density of box x volume of box x acceleration due to gravity
where the density of the box is negligible, so its weight is negligible. Therefore, the weight of the box and the material loaded onto it is given by:
weight = density of water x volume of box x acceleration due to gravity
Substituting the given values, we get:
weight = 1000 kg/m^3 x 5.0 m x 1.0 m x 0.50 m x 9.81 m/s^2
weight = 2.45 x 10^4 N
To convert this to kilograms, we divide by the acceleration due to gravity:
mass = weight / acceleration due to gravity
mass = 2.45 x 10^4 N / 9.81 m/s^2
mass = 2.50 x 10^3 kg
Therefore, the maximum mass of material that can be loaded onto the box before it sinks is 2.50 x 10^3 kg, which is closest to option C: 2.5 × 10^3 kg.

A Rectangular Box of Negligible Mass Measures 5