{"id":87934,"date":"2025-06-01T06:58:07","date_gmt":"2025-06-01T06:58:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87934"},"modified":"2025-06-01T06:58:07","modified_gmt":"2025-06-01T06:58:07","slug":"a-particle-is-moving-in-a-circle-of-radius-r-with-a-constant-speed-v","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-moving-in-a-circle-of-radius-r-with-a-constant-speed-v\/","title":{"rendered":"A particle is moving in a circle of radius R with a constant speed v."},"content":{"rendered":"

A particle is moving in a circle of radius R with a constant speed v. Its average acceleration over the time when it moves over half the circle is :<\/p>\n

[amp_mcq option1=”$\\frac{v^2}{R}$” option2=”$\\frac{\\pi v^2}{2R}$” option3=”$\\frac{2v^2}{\\pi R}$” option4=”0″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is C.
\n<\/section>\n
\nAverage acceleration is defined as the change in velocity divided by the time taken. For a particle moving in a circle with constant speed, the velocity vector changes direction continuously. Over half a circle, the initial and final velocity vectors are in opposite directions.
\n<\/section>\n
\nLet the particle start at $\\theta=0$ (position vector $R\\hat{i}$) and move counter-clockwise. The initial velocity is $\\vec{v}_i = v\\hat{j}$. After moving half a circle ($\\pi$ radians), it is at $\\theta=\\pi$ (position vector $-R\\hat{i}$). The final velocity is $\\vec{v}_f = -v\\hat{j}$. The change in velocity is $\\Delta\\vec{v} = \\vec{v}_f – \\vec{v}_i = -v\\hat{j} – v\\hat{j} = -2v\\hat{j}$. The magnitude of the change in velocity is $|\\Delta\\vec{v}| = 2v$. The distance covered is half the circumference, $\\pi R$. The time taken is $t = (\\pi R) \/ v$. The average acceleration is $\\vec{a}_{avg} = \\Delta\\vec{v}\/t = (-2v\\hat{j}) \/ (\\pi R \/ v) = -\\frac{2v^2}{\\pi R}\\hat{j}$. The magnitude of the average acceleration is $|\\vec{a}_{avg}| = \\frac{2v^2}{\\pi R}$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A particle is moving in a circle of radius R with a constant speed v. Its average acceleration over the time when it moves over half the circle is : [amp_mcq option1=”$\\frac{v^2}{R}$” option2=”$\\frac{\\pi v^2}{2R}$” option3=”$\\frac{2v^2}{\\pi R}$” option4=”0″ correct=”option3″] This question was previously asked in UPSC NDA-1 – 2023 Download PDFAttempt Online The correct option is … <\/p>\n

Detailed SolutionA particle is moving in a circle of radius R with a constant speed v.<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1105,1129,1128],"class_list":["post-87934","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1105","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA particle is moving in a circle of radius R with a constant speed v.<\/title>\n<meta name=\"description\" content=\"The correct option is C. Average acceleration is defined as the change in velocity divided by the time taken. For a particle moving in a circle with constant speed, the velocity vector changes direction continuously. Over half a circle, the initial and final velocity vectors are in opposite directions.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-moving-in-a-circle-of-radius-r-with-a-constant-speed-v\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A particle is moving in a circle of radius R with a constant speed v.\" \/>\n<meta property=\"og:description\" content=\"The correct option is C. Average acceleration is defined as the change in velocity divided by the time taken. For a particle moving in a circle with constant speed, the velocity vector changes direction continuously. 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