{"id":7149,"date":"2024-04-15T02:40:20","date_gmt":"2024-04-15T02:40:20","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7149"},"modified":"2024-04-15T02:40:20","modified_gmt":"2024-04-15T02:40:20","slug":"if-a-sphere-of-diameter-1-cm-falls-in-castor-oil-of-kinematic-viscosity-10-stokes-with-a-terminal-velocity-of-1-5-cm-sec-the-coefficient-of-drag-on-the-sphere-is-a-less-than-1-b-between-1-and-100","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-a-sphere-of-diameter-1-cm-falls-in-castor-oil-of-kinematic-viscosity-10-stokes-with-a-terminal-velocity-of-1-5-cm-sec-the-coefficient-of-drag-on-the-sphere-is-a-less-than-1-b-between-1-and-100\/","title":{"rendered":"If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm\/sec, the coefficient of drag on the sphere is A. less than 1 B. between 1 and 100 C. 160 D. 200"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;less than 1&#8243; option2=&#8221;between 1 and 100&#8243; option3=&#8221;160&#8243; option4=&#8221;200&#8243; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is A. less than 1.<\/p>\n<p>The drag coefficient is a dimensionless number that characterizes the aerodynamic drag (or in this case, hydrodynamic drag) of a body in a fluid environment, and is used in the drag equation. It is defined as the ratio of the drag force to the dynamic pressure times the frontal area of the body.<\/p>\n<p>The drag force on a sphere in a fluid is given by the following equation:<\/p>\n<p>$F_d = \\frac{1}{2} \\rho C_d A v^2$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\rho$ is the density of the fluid<\/li>\n<li>$C_d$ is the drag coefficient<\/li>\n<li>$A$ is the frontal area of the sphere<\/li>\n<li>$v$ is the velocity of the sphere<\/li>\n<\/ul>\n<p>The terminal velocity of a sphere in a fluid is given by the following equation:<\/p>\n<p>$v_t = \\sqrt{\\frac{2mg}{\\rho C_d A}}$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$m$ is the mass of the sphere<\/li>\n<li>$g$ is the acceleration due to gravity<\/li>\n<\/ul>\n<p>Given the following information:<\/p>\n<ul>\n<li>Diameter of the sphere: $d = 1 \\text{ cm}$<\/li>\n<li>Kinematic viscosity of castor oil: $\\mu = 10 \\text{ stokes}$<\/li>\n<li>Terminal velocity of the sphere: $v_t = 1.5 \\text{ cm\/s}$<\/li>\n<\/ul>\n<p>We can calculate the drag coefficient as follows:<\/p>\n<p>$C_d = \\frac{2mg}{\\rho A v_t^2} = \\frac{2 \\times 0.001 \\times 9.8}{0.914 \\times 0.01 \\times 1.5^2} = 0.0014$<\/p>\n<p>Therefore, the drag coefficient is less than 1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;less than 1&#8243; option2=&#8221;between 1 and 100&#8243; option3=&#8221;160&#8243; option4=&#8221;200&#8243; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[648],"tags":[],"class_list":["post-7149","post","type-post","status-publish","format-standard","hentry","category-hydraulics-and-fluid-mechanics","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If a sphere of diameter 1 cm falls in castor oil 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