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Q.1

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Found in: Page 555

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.(a) Mass and weight are the same.(b) A large object can have less mass than a smaller object.(c) An object can have one mass on Earth and another mass on the moon.(d) An object can have one weight on Earth and another weight on the moon.(e) Water has a weight-density of 62.4 foot pounds.(f) It always takes more work to lift a heavy object than a light object for the same distance.(g) Hydrostatic force can be measured only on horizontal walls.(h) Hydrostatic force is stronger at greater depths than it is at lesser depths.

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See the step by step solution

## Step 1. Given Information

Given to determine whether each of the statements below is true or false. If a statement is true, the reason is to be explained. If a statement is false, a counterexample is to be provided.

(a) Mass and weight are the same.

(b) A large object can have less mass than a smaller object.

(c) An object can have one mass on Earth and another mass on the moon.

(d) An object can have one weight on Earth and another weight on the moon.

(e) Water has a weight-density of 62.4 foot pounds.

(f) It always takes more work to lift a heavy object than a light object for the same distance.

(g) Hydrostatic force can be measured only on horizontal walls.

(h) Hydrostatic force is stronger at greater depths than it is at lesser depths.

## Part (a) Step 1. Verifying the statement

Given statement is: Mass and weight are the same.

Mass represents the amount of matter in the object whereas weight is the gravitational pull on the object.

Hence the given statement is false.

## Part (b) Step 1. Verifying the statement

Given statement is: A large object can have less mass than a smaller object.

Mass is the amount of matter in an object. Hence a large object has larger mass and a smaller object has lesser mass.

Hence the given statement is false.

## Part (c) Step 1. Verifying the statement

Given statement is: An object can have one mass on Earth and another mass on the moon.

Mass is the amount of matter in an object. So, irrespective of the location the mass of an object always remains the same.

Hence the given statement is false.

## Part (d) Step 1. Verifying the statement

Given statement is: An object can have one weight on Earth and another weight on the moon.

Weight is the gravitational pull on the object. But the gravity in the moon is different than Earth. So there can be different weights for an object on Earth and on Moon.

Hence the given statement is true.

## Part (e) Step 1. Verifying the statement

Given statement is: Water has a weight-density of 62.4 foot pounds.

The unit of density is weight per volume. Here the units are not correct.

Hence the given statement is false.

## Part (f) Step 1. Verifying the statement

Given statement is: It always takes more work to lift a heavy object than a light object for the same distance.

The work done in lifting an object is to overcome the force of gravity. The force of gravity on an heavy object is greater than the force on light object. So the work done to lift heavy object is more than the work done to lift a light object for the same distance.

Hence the given statement is true.

## Part (g) Step 1. Verifying the statement

Given statement is: Hydrostatic force can be measured only on horizontal walls.

Hydrostatic force is the force exerted by a fluid due to the force on gravity. Hence this pressure is also applied on the walls of the container apart from downward force.

Hence the given statement is false.

## Part (h) Step 1. Verifying the statement

Given statement is: Hydrostatic force is stronger at greater depths than it is at lesser depths.

Hydrostatic force is the force applied by the water on the surfaces. So at greater depts the water above the surface is more and hence the hydrostatic force is stronger at greater depths.

Hence the given statement is true.