{"id":37000,"date":"2025-06-25T11:15:32","date_gmt":"2025-06-25T11:15:32","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37000"},"modified":"2025-06-25T11:15:33","modified_gmt":"2025-06-25T11:15:33","slug":"the-student-attempt-to-measure-the-diameter-of-a-steel-ball-by-using-meter-rule-to-measure-four-similar-ball-in-a-row","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-student-attempt-to-measure-the-diameter-of-a-steel-ball-by-using-meter-rule-to-measure-four-similar-ball-in-a-row\/","title":{"rendered":"The student attempt to measure the diameter of a steel ball by using meter rule to measure four similar ball in a row"},"content":{"rendered":"\n

The student attempt to measure the diameter of a steel ball by using meter rule to measure four similar ball in a row. – cm 0 2 3 4 6 5 The student estimate the positions on the scale to be as follows. X (1.0 20.2) cm Y(5.0 +0.2) cm What is the diameter of a steel ball together with its associated uncertainty? A) (1.0 20.05) cm C) (1.0 +0.1) cm B) (1.0 +0.2) cm D) (1.0 +0.24) cm<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the diameter of a single steel ball and its associated uncertainty, we follow a simple physics measurement method using the meter rule<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Given:<\/strong><\/h3>\n\n\n\n
    \n
  • Four<\/strong> steel balls are measured in a row<\/strong>.<\/li>\n\n\n\n
  • The student recorded:\n
      \n
    • X = (1.0 \u00b1 0.2) cm<\/strong><\/li>\n\n\n\n
    • Y = (5.0 \u00b1 0.2) cm<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

      These are the positions of the ends<\/strong> of the four balls on the meter rule.<\/p>\n\n\n\n

      \n\n\n\n

      Step 1: Calculate the total length occupied by the four balls<\/strong><\/h3>\n\n\n\n

      Length=Y\u2212X=5.0 cm\u22121.0 cm=4.0 cm\\text{Length} = Y – X = 5.0\\ \\text{cm} – 1.0\\ \\text{cm} = 4.0\\ \\text{cm}Length=Y\u2212X=5.0 cm\u22121.0 cm=4.0 cm<\/p>\n\n\n\n

      \n\n\n\n

      Step 2: Find the diameter of one steel ball<\/strong><\/h3>\n\n\n\n

      Since the total length is for 4 balls<\/strong>, the diameter of one ball is:Diameter=4.0 cm4=1.0 cm\\text{Diameter} = \\frac{4.0\\ \\text{cm}}{4} = 1.0\\ \\text{cm}Diameter=44.0 cm\u200b=1.0 cm<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Calculate uncertainty<\/strong><\/h3>\n\n\n\n

      Each position (X and Y) has an uncertainty of \u00b10.2 cm. When subtracting measurements with uncertainties, you add the uncertainties<\/strong>:Uncertainty in total length=0.2 cm+0.2 cm=0.4 cm\\text{Uncertainty in total length} = 0.2\\ \\text{cm} + 0.2\\ \\text{cm} = 0.4\\ \\text{cm}Uncertainty in total length=0.2 cm+0.2 cm=0.4 cm<\/p>\n\n\n\n

      Now, divide this by 4 to get the uncertainty of the diameter of one ball:Uncertainty in diameter=0.4 cm4=0.1 cm\\text{Uncertainty in diameter} = \\frac{0.4\\ \\text{cm}}{4} = 0.1\\ \\text{cm}Uncertainty in diameter=40.4 cm\u200b=0.1 cm<\/p>\n\n\n\n

      \n\n\n\n

      Final Answer:<\/strong><\/h3>\n\n\n\n

      (1.0\u00b10.1) cm\\boxed{(1.0 \\pm 0.1)\\ \\text{cm}}(1.0\u00b10.1) cm\u200b<\/p>\n\n\n\n

      \n\n\n\n

      Explanation<\/strong><\/h3>\n\n\n\n

      To find the diameter of one steel ball, the student used a common technique in experimental physics: measure multiple similar items together, then divide the total length by the number of items. This method reduces relative error<\/strong> and increases accuracy<\/strong>, especially when each individual item is small compared to the least count of the measuring instrument.<\/p>\n\n\n\n

      Here, four steel balls were aligned in a straight line. The student read the position of one end as (1.0 \u00b1 0.2) cm and the other end as (5.0 \u00b1 0.2) cm. These are X and Y, and the difference between Y and X gives the total length of the four balls: 4.0 cm. Dividing this by 4, each ball\u2019s diameter is 1.0 cm.<\/p>\n\n\n\n

      Uncertainty is also crucial. Since both measurements X and Y have a \u00b10.2 cm uncertainty, the uncertainty in the total length is 0.4 cm. We then divide this total uncertainty by 4 (the number of balls) to find the uncertainty in one diameter measurement, giving \u00b10.1 cm.<\/p>\n\n\n\n

      Therefore, the diameter of a single steel ball is best expressed as (1.0 \u00b1 0.1) cm.<\/p>\n\n\n\n

      \n\n\n\n

      \u2705 Correct Choice:<\/strong><\/h3>\n\n\n\n

      C) (1.0 \u00b1 0.1) cm<\/strong><\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      The student attempt to measure the diameter of a steel ball by using meter rule to measure four similar ball in a row. – cm 0 2 3 4 6 5 The student estimate the positions on the scale to be as follows. X (1.0 20.2) cm Y(5.0 +0.2) cm What is the diameter of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37000","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37000","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37000"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37000\/revisions"}],"predecessor-version":[{"id":37002,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37000\/revisions\/37002"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37000"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37000"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37000"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}