{"id":541964,"date":"2023-04-23T05:30:22","date_gmt":"2023-04-23T00:00:22","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-tortoise-is-just-sinking-in-water-of-density-%cf%81-the-tortoise-is-assumed-to-be-a-hemisphere-of-radius-r-2\/"},"modified":"2025-06-20T15:17:08","modified_gmt":"2025-06-20T09:47:08","slug":"a-tortoise-is-just-sinking-in-water-of-density-%cf%81-the-tortoise-is-assumed-to-be-a-hemisphere-of-radius-r-2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/","title":{"rendered":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.","custom_permalink":"question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/"},"categories":[],"acf":{"question":"<p>A tortoise is just sinking in water of density&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03c1<\/mi><\/math>. The tortoise is assumed to be a hemisphere of radius R.<\/p><figure class=\"image\"><img src=\"data:image\/png;base64,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\"><\/figure>","options":null,"solution":"Let's consider the horizontal and vertical forces, <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>h<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_h<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>v<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_v<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, acting on a tortoise. For the horizontal force <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>h<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_h<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, we understand it as <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>h<\/mi><\/msub><mo>=<\/mo><mi>\u03c1<\/mi><mi>g<\/mi><msub><mi>y<\/mi><mi>C<\/mi><\/msub><msub><mi>A<\/mi><mi>v<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_h = \\rho g y_C A_v<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mord mathnormal\">g<\/span><span class=\"mord\"><span class=\"mord mathnormal\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">C<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>y<\/mi><mi>C<\/mi><\/msub><mo>=<\/mo><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y_C = R<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">C<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>A<\/mi><mi>v<\/mi><\/msub><mo>=<\/mo><mi>\u03c0<\/mi><msup><mi>R<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">A_v = \\pi R^2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">\u03c0<\/span><span class=\"mord\"><span class=\"mord mathnormal\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. This leads to the calculation <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>h<\/mi><\/msub><mo>=<\/mo><mi>\u03c1<\/mi><mi>g<\/mi><mi>\u03c0<\/mi><msup><mi>R<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">F_h = \\rho g \\pi R^3<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mord mathnormal\">g<\/span><span class=\"mord mathnormal\">\u03c0<\/span><span class=\"mord\"><span class=\"mord mathnormal\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, which acts towards the right. Similarly, the vertical force <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>v<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_v<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> can be derived using <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>v<\/mi><\/msub><mo>=<\/mo><mi>\u03c1<\/mi><mi>V<\/mi><mi>g<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">F_v = \\rho V g<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mord mathnormal\">V<\/span><span class=\"mord mathnormal\">g<\/span><\/span><\/span><\/span>, where <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span><\/span>, the volume of the tortoise, is <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>R<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{3} \\pi R^3<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">\u03c0<\/span><span class=\"mord\"><span class=\"mord mathnormal\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Consequently, <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mi>v<\/mi><\/msub><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c1<\/mi><mi>g<\/mi><mi>\u03c0<\/mi><msup><mi>R<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">F_v = \\frac{2}{3} \\rho g \\pi R^3<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">v<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mord mathnormal\">g<\/span><span class=\"mord mathnormal\">\u03c0<\/span><span class=\"mord\"><span class=\"mord mathnormal\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, directed upwards.","subject":"Physics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-20T09:47:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R. - Infinity Learn by Sri Chaitanya","description":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/","og_locale":"en_US","og_type":"article","og_title":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R. - Infinity Learn by Sri Chaitanya","og_description":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.","og_url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-20T09:47:08+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/","name":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R. - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2023-04-23T00:00:22+00:00","dateModified":"2025-06-20T09:47:08+00:00","description":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-tortoise-is-just-sinking-in-water-of-density-the-tortoi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"A tortoise is just sinking in water of density\u00a0\u03c1. The tortoise is assumed to be a hemisphere of radius R."}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/541964"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=541964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=541964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}