{"id":259574,"date":"2022-09-10T12:16:28","date_gmt":"2022-09-10T06:46:28","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-system-consists-of-three-masses-m1-m2-and-m3-connected-by-a-string-passing-over-a-pulley-p-the-mass-m1-hangs-freely-and-m2-and-m3-are-on-a-r\/"},"modified":"2022-09-10T12:16:28","modified_gmt":"2022-09-10T06:46:28","slug":"a-system-consists-of-three-masses-m1-m2-and-m3-connected-by-a-string-passing-over-a-pulley-p-the-mass-m1-hangs-freely-and-m2-and-m3-are-on-a-r","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-system-consists-of-three-massesm1m2andm3-connected-b\/","title":{"rendered":"A system consists of three masses\u00a0m1,\u00a0m2\u00a0and\u00a0m3\u00a0 connected by a string passing over a pulley P. The mass\u00a0m1\u00a0hangs freely and\u00a0m2\u00a0and\u00a0m3\u00a0are on a rough horizontal table (the coefficient of friction=\u00a0\u03bc)The pulley is frictionless and of negligible mass. The downward acceleration of mass\u00a0m1\u00a0is\u00a0\u00a0(Assume\u00a0m1=m2=m3=m\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A system consists of three masses\u00a0m1,\u00a0m2\u00a0and\u00a0m3\u00a0 connected by a string passing over a pulley P. The mass\u00a0m1\u00a0hangs freely and\u00a0m2\u00a0and\u00a0m3\u00a0are on a rough horizontal table (the coefficient of friction=\u00a0\u03bc)The pulley is frictionless and of negligible mass. The downward acceleration of mass\u00a0m1\u00a0is\u00a0\u00a0(Assume\u00a0m1=m2=m3=m\u00a0","custom_permalink":"question\/physics\/a-system-consists-of-three-massesm1m2andm3-connected-b\/"},"categories":[],"acf":{"question":"

A system consists of three masses m<\/mi>1<\/mn><\/msub>,<\/mo> <\/mo>m<\/mi>2<\/mn><\/msub> <\/mo>a<\/mi>n<\/mi>d<\/mi> <\/mo>m<\/mi>3<\/mn><\/msub><\/math>  connected by a string passing over a pulley P. The mass m<\/mi>1<\/mn><\/msub><\/math> hangs freely and m<\/mi>2<\/mn><\/msub><\/math> and m<\/mi>3<\/mn><\/msub><\/math> are on a rough horizontal table (the coefficient of friction= \u03bc<\/mi><\/math>)<\/p>

The pulley is frictionless and of negligible mass. The downward acceleration of mass m<\/mi>1<\/mn><\/msub><\/math> is <\/p>

 (Assume <\/mtext>m<\/mi>1<\/mn><\/msub>=<\/mo>m<\/mi>2<\/mn><\/msub>=<\/mo>m<\/mi>3<\/mn><\/msub>=<\/mo>m<\/mi><\/mrow><\/mfenced><\/math><\/p>
<\/figure>

 <\/p>","options":[{"option":"

g<\/mi>(<\/mo>1<\/mn>\u2212<\/mo>g<\/mi>\u03bc<\/mi>)<\/mo><\/mrow>9<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

2<\/mn>g<\/mi>\u03bc<\/mi><\/mrow>3<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

g<\/mi>(<\/mo>1<\/mn>\u2212<\/mo>2<\/mn>\u03bc<\/mi>)<\/mo><\/mrow>3<\/mn><\/mfrac><\/math><\/p>","correct":true},{"option":"

g<\/mi>(<\/mo>1<\/mn>\u2212<\/mo>2<\/mn>\u03bc<\/mi>)<\/mo><\/mrow>2<\/mn><\/mfrac><\/math><\/p>","correct":false}],"solution":"
<\/figure>

Force of friction on mass m<\/mi>2<\/mn><\/msub>=<\/mo>\u03bc<\/mi>m<\/mi>2<\/mn><\/msub>g<\/mi><\/math>        <\/p>

Force of friction on mass     m<\/mi>3<\/mn><\/msub>=<\/mo>\u03bc<\/mi>m<\/mi>3<\/mn><\/msub>g<\/mi><\/math>        <\/p>

Let \u03b1<\/mi><\/math> be common acceleration of the system.<\/p>

\u2234<\/mo> <\/mspace>a<\/mi>=<\/mo>m<\/mi>1<\/mn><\/msub>g<\/mi>\u2212<\/mo>\u03bc<\/mi>m<\/mi>2<\/mn><\/msub>g<\/mi>\u2212<\/mo>\u03bc<\/mi>m<\/mi>3<\/mn><\/msub>g<\/mi><\/mrow>m<\/mi>1<\/mn><\/msub>+<\/mo>m<\/mi>2<\/mn><\/msub>+<\/mo>m<\/mi>3<\/mn><\/msub><\/mrow><\/mfrac><\/math><\/p>

 Here, <\/mtext>m<\/mi>1<\/mn><\/msub>=<\/mo>m<\/mi>2<\/mn><\/msub>=<\/mo>m<\/mi>3<\/mn><\/msub>=<\/mo>m<\/mi><\/math><\/p>

 Hence, the downward acceleration of mass <\/mtext>m<\/mi>1<\/mn><\/msub> is <\/mtext><\/mtd><\/mtr>g<\/mi>(<\/mo>1<\/mn>\u2212<\/mo>2<\/mn>\u03bc<\/mi>)<\/mo><\/mrow>3<\/mn><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/p>

 <\/p>","subject":""},"yoast_head":"\nA system consists of three masses\u00a0m1,\u00a0m2\u00a0and\u00a0m3\u00a0 connected by a string passing over a pulley P. The mass\u00a0m1\u00a0hangs freely and\u00a0m2\u00a0and\u00a0m3\u00a0are on a rough horizontal table (the coefficient of friction=\u00a0\u03bc)The pulley is frictionless and of negligible mass. The downward acceleration of mass\u00a0m1\u00a0is\u00a0\u00a0(Assume\u00a0m1=m2=m3=m\u00a0 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A system consists of three masses\u00a0m1,\u00a0m2\u00a0and\u00a0m3\u00a0 connected by a string passing over a pulley P. The mass\u00a0m1\u00a0hangs freely and\u00a0m2\u00a0and\u00a0m3\u00a0are on a rough horizontal table (the coefficient of friction=\u00a0\u03bc)The pulley is frictionless and of negligible mass. 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