Milk has a viscosity of about 2.1 cp at 20 C. The density of whole milk is about 1.03 g\/cc and milk fat (cream) has a density of about .93 g\/cc and the average drop of cream has an 8 \u03bc diameter. Use Stokes's law to calculate how long it will take a drop of cream to rise 10 cm. O 12 hr 40 min O 16 hr 45 min 6000 sec O 10 hr 45 min<\/p>\n\n\n\n
The Correct Answer and Explanation is <\/strong><\/mark><\/p>\n\n\n\n The correct answer is 16 hours 45 minutes<\/strong>.<\/p>\n\n\n\n To determine how long it takes for a drop of cream (fat) to rise through milk, we use Stokes’ Law<\/strong>, which applies to small spheres moving through a viscous fluid. The formula for the terminal velocity of a small sphere in a fluid is:<\/p>\n\n\n\n [ where:<\/p>\n\n\n\n The given drop of cream has a diameter<\/strong> of 8 \u03bcm<\/strong> (or ( 8 \\times 10^{-6} ) m), so its radius<\/strong> is:<\/p>\n\n\n\n [ Plugging in the values:<\/p>\n\n\n\n [ [ To rise 10 cm (0.1 m)<\/strong>:<\/p>\n\n\n\n [ Converting:<\/p>\n\n\n\n [ Thus, the correct answer is 16 hours 45 minutes<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Milk has a viscosity of about 2.1 cp at 20 C. The density of whole milk is about 1.03 g\/cc and milk fat (cream) has a density of about .93 g\/cc and the average drop of cream has an 8 \u03bc diameter. Use Stokes's law to calculate how long it will take a drop of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-187711","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187711","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=187711"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187711\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187711"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187711"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
v = \\frac{2}{9} \\frac{r^2 g (\\rho_m – \\rho_c)}{\\mu}
]<\/p>\n\n\n\n\n
r = \\frac{8 \\times 10^{-6}}{2} = 4 \\times 10^{-6} \\text{ m}
]<\/p>\n\n\n\n
v = \\frac{2}{9} \\times \\frac{(4 \\times 10^{-6})^2 \\times 9.81 \\times (1030 – 930)}{2.1 \\times 10^{-3}}
]<\/p>\n\n\n\n
v = 1.66 \\times 10^{-6} \\text{ m\/s}
]<\/p>\n\n\n\n
t = \\frac{0.1}{1.66 \\times 10^{-6}} = 60226.99 \\text{ seconds}
]<\/p>\n\n\n\n
60226.99 \\text{ s} = 16 \\text{ hours } 45 \\text{ minutes}
]<\/p>\n\n\n\n