Hướng dẫn giải Luyện tập 3 (Trang 22 SGK Vật lý 10, Bộ Chân trời sáng tạo)

Giả sử chiều dài của hai đoạn thẳng có giá trị đo được lần lượt là <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>51</mn><mo>&#xB1;</mo><mn>1</mn><mtext>&#x2009;</mtext><mi>c</mi><mi>m</mi></math>">a=51±1cm và <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>49</mn><mo>&#xB1;</mo><mn>1</mn><mtext>&#x2009;</mtext><mi>c</mi><mi>m</mi></math>">b=49±1cm . Trong các đại lượng được tính theo các cách sau đây, đại lượng nào có sai số tương đối lớn nhất: A. a + b . B. a - b. C. a x b. D. <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a</mi><mi>b</mi></mfrac></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a</mi><mi>b</mi></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi></mi></mfrac></math>. Lời giải: Đáp án đúng là: B Từ a = 51±1cm => <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>a</mi><mo>&#xAF;</mo></mover></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>a</mi></menclose></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mo></mo></mover></math> = 51cm; ∆a = 1cm; b = 49±1cm => <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>b</mi><mo>&#xAF;</mo></mover></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>b</mi></menclose></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mo></mo></mover></math> = 49cm; ∆b = 1cm; Ta xét các trường hợp: + Với biểu thức (a + b) có sai số là <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mo> </mo><mi>F</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>F</mi></mrow><mi>F</mi></mfrac><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>a</mi><mo> </mo><mo>+</mo><mo> </mo><mi>Δ</mi><mo> </mo><mi>b</mi></mrow><mrow><menclose notation="top"><mi>a</mi></menclose><mo>+</mo><menclose notation="top"><mi>b</mi></menclose></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow><mrow><mn>51</mn><mo>+</mo><mn>49</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>,</mo><mn>02</mn><mi>c</mi><mi>m</mi></math> + Với biểu thức (a – b) có sai số là <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mo> </mo><mi>F</mi><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>F</mi></mrow><mi>F</mi></mfrac><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>a</mi><mo> </mo><mo>+</mo><mo> </mo><mi>Δ</mi><mo> </mo><mi>b</mi></mrow><mrow><menclose notation="top"><mi>a</mi></menclose><mo>-</mo><menclose notation="top"><mi>b</mi></menclose></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow><mrow><mn>51</mn><mo>-</mo><mn>49</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mi>c</mi><mi>m</mi></math> + Với biểu thức (a x b) và  <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a</mi><mi>b</mi></mfrac></math>"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a</mi><mi>b</mi></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi></mi></mfrac></math> đều có sai số là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mo> </mo><mi>F</mi><mo>=</mo><mi>δ</mi><mo> </mo><mi>a</mi><mo> </mo><mo>+</mo><mo> </mo><mi>δ</mi><mo> </mo><mi>b</mi><mo> </mo><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>a</mi></mrow><menclose notation="top"><mi>a</mi></menclose></mfrac><mo>=</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>a</mi><mo> </mo></mrow><menclose notation="top"><mi>a</mi></menclose></mfrac><mo>+</mo><mfrac><mrow><mi>Δ</mi><mo> </mo><mi>b</mi><mo> </mo></mrow><menclose notation="top"><mi>b</mi></menclose></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>51</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>49</mn></mfrac><mo>=</mo><mn>0</mn><mo>,</mo><mn>04</mn><mi>c</mi><mi>m</mi></math>

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