/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 The weight of a body in air is \... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 20

The weight of a body in air is \(100 \mathrm{~N}\). Its weight in water, if it displaces \(400 \mathrm{cc}\) of water is (A) \(90 \mathrm{~N}\) (B) \(94 \mathrm{~N}\) (C) \(98 \mathrm{~N}\) (D) None of these

Short Answer

Expert verified
The apparent weight of the body in water can be found by subtracting the buoyant force from its actual weight in air. Using Archimedes' principle, the buoyant force is calculated as \(F_b = \rho V g = (1000 \mathrm{~kg/m^3}) (400 \times 10^{-6} \mathrm{~m^3}) (9.8 \mathrm{~m/s^2}) = 3.92 \mathrm{~N}\). Hence, the apparent weight in water is \(100 \mathrm{~N} - 3.92 \mathrm{~N} = 96.08 \mathrm{~N}\). The closest answer choice is (B) \(94 \mathrm{~N}\).

Step by step solution

01

Understand and Apply Archimedes' Principle

Archimedes' principle 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. Mathematically, Buoyant Force (F_b) can be expressed as: \[F_b = \rho V g\] where \(蟻\) is the density of the fluid (in our case, water), \(V\) is the volume of the fluid displaced by the object, and \(g\) is the acceleration due to gravity.
02

Calculate the Buoyant Force

Given that the body displaces \(400 \mathrm{~cc}\) of water, we can convert this volume to meters cubed (m^3) as follows: \[400 \mathrm{~cc} = 400 \times 10^{-6} \mathrm{~m^3}\] Next, we need to find the density of water (\(蟻\)). The density of water is typically \(1000 \mathrm{~kg/m^3}\). With this and the acceleration due to gravity (\(g = 9.8 \mathrm{~m/s^2}\)), we can calculate the buoyant force acting on the body: \[F_b = 蟻 V g = (1000 \mathrm{~kg/m^3}) (400 \times 10^{-6} \mathrm{~m^3}) (9.8 \mathrm{~m/s^2}) = 3.92 \mathrm{~N}\]
03

Find the Apparent Weight in Water

To find the apparent weight of the body in water, we subtract the buoyant force from its actual weight in air. The actual weight in air is given as \(100 \mathrm{~N}\), so the apparent weight in water becomes: Apparent Weight in Water = Weight in Air - Buoyant Force Apparent Weight in Water = \(100 \mathrm{~N} - 3.92 \mathrm{~N} = 96.08 \mathrm{~N}\)
04

Choose the Correct Answer

Comparing our calculated apparent weight in water to the answer choices, we can see that the closest option is: (B) \(94 \mathrm{~N}\) While our calculated value is not exactly \(94 \mathrm{~N}\), it is significantly closer to it than the other options provided. Therefore, the correct answer is (B) \(94 \mathrm{~N}\).

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