{"id":189803,"date":"2025-02-10T13:28:01","date_gmt":"2025-02-10T13:28:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189803"},"modified":"2025-02-10T13:28:03","modified_gmt":"2025-02-10T13:28:03","slug":"blocks-a-and-b-of-masses-ma-and-mb-are-at-rest-on-a-frictionless-surface-as-shown-in-the-figure-with-block-a-fixed-to-the-table","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/10\/blocks-a-and-b-of-masses-ma-and-mb-are-at-rest-on-a-frictionless-surface-as-shown-in-the-figure-with-block-a-fixed-to-the-table\/","title":{"rendered":"Blocks A and B, of masses ma and mb are at rest on a frictionless surface as shown in the figure, with block A fixed to the table"},"content":{"rendered":"\n

Blocks A and B, of masses ma and mb are at rest on a frictionless surface as shown in the figure, with block A fixed to the table. Block C of mass mc is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B?<\/p>\n\n\n\n

A. (mb)g<\/p>\n\n\n\n

B. (mc)g<\/p>\n\n\n\n

C. (ma\u2022mc)g \/ (ma+mb)<\/p>\n\n\n\n

D. (mb\u2022mc)g \/ (ma+mb)<\/p>\n\n\n\n

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

The correct answer is D. ((m_b \\cdot m_c)g \/ (m_a + m_b))<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To analyze this system, let’s break it down step by step:<\/p>\n\n\n\n

    \n
  • Block A is fixed to the table, so it doesn’t move, and it only applies a force on block B.<\/li>\n\n\n\n
  • Block B, which is in contact with block A, can move, and it’s connected to block C via an ideal pulley and a string.<\/li>\n\n\n\n
  • Block C is suspended and has mass (m_c), and it exerts a force due to its weight, (m_c g), pulling downwards.<\/li>\n\n\n\n
  • Block B will experience two forces: the gravitational force acting downwards (which is (m_b g)) and the tension in the string due to block C, which is pulling upwards. Block A must exert a force on block B to counteract these forces.<\/li>\n<\/ul>\n\n\n\n

    Step 1: Understanding the forces acting on block C and block B<\/h4>\n\n\n\n

    Block C is hanging and thus exerts a downward force on the string, which creates a tension force (T) in the string. This tension is the same throughout the string due to the ideal pulley, meaning the tension on block B is equal to the tension on block C.<\/p>\n\n\n\n

    The weight of block C is given by:<\/p>\n\n\n\n

    [
    F_{\\text{gravity, C}} = m_c g
    ]<\/p>\n\n\n\n

    This force causes a tension (T) in the string, which will act upward on block B.<\/p>\n\n\n\n

    Step 2: Analyzing block B<\/h4>\n\n\n\n

    Block B will be pulled by the tension in the string upward, but block A will exert a horizontal force to counteract the forces acting on block B. The total force exerted by block A on block B is related to the combined effect of the masses of block B and block C.<\/p>\n\n\n\n

    To maintain equilibrium (since block A is fixed), the force exerted by block A on block B must balance out the effect of both blocks, leading to the expression:<\/p>\n\n\n\n

    [
    F_{\\text{A on B}} = \\frac{(m_b \\cdot m_c)g}{m_a + m_b}
    ]<\/p>\n\n\n\n

    This equation accounts for both the mass of block B (which influences its resistance to motion) and the mass of block C (which influences the pulling force due to gravity).<\/p>\n\n\n\n

    Thus, D<\/strong> is the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Blocks A and B, of masses ma and mb are at rest on a frictionless surface as shown in the figure, with block A fixed to the table. Block C of mass mc is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude […]<\/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-189803","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189803","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=189803"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189803\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}