/*! 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 45 A uniform metre scale balances a... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 45

A uniform metre scale balances at the \(40 \mathrm{~cm}\) mark when weight of \(10 \mathrm{~g}\) and \(20 \mathrm{~g}\) are suspended from the \(10 \mathrm{~cm}\) and \(20 \mathrm{~cm}\) marks. The weight of the metre scale is (A) \(50 \mathrm{~g}\) (B) \(60 \mathrm{~g}\) (C) \(70 \mathrm{~g}\) (D) \(80 \mathrm{~g}\)

Short Answer

Expert verified
The weight of the meter scale is 70 g.

Step by step solution

01

Identify the torques for the meter scale

First, we must identify the torques experienced by the uniform meter scale. We have three forces acting on the meter scale: 1. The weight of the meter scale (W) applied at its center of mass (50 cm mark) 2. The weight of the 10 g mass (10 g) applied at the 10 cm mark 3. The weight of the 20 g mass (20 g) applied at the 20 cm mark
02

Torque balance equation

We can write the torque balance equation as follows: Torque_due_to_W + Torque_due_to_10g + Torque_due_to_20g = 0 For a uniform meter scale, the center of mass will be at the middle point, which is at the 50 cm mark. Since the scale balances at the 40 cm mark, the distance to each of the weights for torque calculation should be relative to the 40 cm mark. For W, this distance is 10 cm; for the 10g weight, it is 30 cm; and for the 20g weight, it is 20 cm.
03

Calculate the torques

To calculate the torque, we use the formula: Torque = Force 脳 Distance 脳 sin(angle) Since all the weights are acting vertically downward, we have sin(angle) = 1. Substituting all the values in the equation, we get: Torque_due_to_W = W 脳 10 cm Torque_due_to_10g = 10 g 脳 30 cm Torque_due_to_20g = 20 g 脳 20 cm
04

Solve for the weight of the meter scale

Now, we can substitute the torques back into the torque balance equation: (W 脳 10 cm) + (10 g 脳 30 cm) + (20 g 脳 20 cm) = 0 We need to solve for W: 10W = 300g + 400g 10W = 700g Therefore, the weight of the meter scale, W, is: W = 70g So, the correct answer is: (C) 70 g

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Most popular questions from this chapter

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