{"id":624713,"date":"2023-06-21T01:52:29","date_gmt":"2023-06-20T20:22:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-force-of-5-n-produces-an-acceleration-of-8-ms-2-on-mass-m1-and-an-acceleration-of-24-ms-2-on-mass-m2-what-is-the-acceleration-if-both-the-masses-are-tied-together\/"},"modified":"2025-06-26T18:00:37","modified_gmt":"2025-06-26T12:30:37","slug":"a-force-of-5-n-produces-an-acceleration-of-8-ms-2-on-mass-m1-and-an-acceleration-of-24-ms-2-on-mass-m2-what-is-the-acceleration-if-both-the-masses-are-tied-together","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-force-of-5n-produces-an-acceleration-of-8ms-2-on-mass-m1\/","title":{"rendered":"A force of 5\u00a0N produces an acceleration of 8\u00a0ms-2 on mass m1 and an acceleration of 24\u00a0ms-2 on mass m2. What is the acceleration, if both the masses are tied together?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A force of 5\u00a0N produces an acceleration of 8\u00a0ms-2 on mass m1 and an acceleration of 24\u00a0ms-2 on mass m2. What is the acceleration, if both the masses are tied together?","custom_permalink":"question\/physics\/a-force-of-5n-produces-an-acceleration-of-8ms-2-on-mass-m1\/"},"categories":[],"acf":{"question":"

A force of <\/span>5<\/mn> <\/mi>N<\/mi><\/math> produces an acceleration of <\/span>8<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> on mass <\/span>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/math> and an acceleration of <\/span>24<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> on mass <\/span>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math>. What is the acceleration, if both the masses are tied together?<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;page-break-inside:avoid;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';color:#202124;-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;page-break-inside:avoid;line-height:normal;font-size:12pt\">","options":[{"option":"5<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> <\/span>","correct":false},{"option":"6<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> <\/span>","correct":true},{"option":"7<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> <\/span>","correct":false},{"option":"8<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> <\/span> <\/span>","correct":false}],"solution":"A force of <\/span>5<\/mn> <\/mi>N<\/mi><\/math> produces an acceleration of <\/span>8<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> on mass <\/span>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/math> and an acceleration of <\/span>24<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> on mass <\/span>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math>. The acceleration is <\/span>6<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> if both the masses are tied together.<\/span>
Given, <\/span>
Force of the first mass, <\/span>F<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>5<\/mn> <\/mi>N<\/mi><\/math>
acceleration of first mass, <\/span>a<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>8<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math>
Force of second mass, <\/span>F<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>5<\/mn> <\/mi>N<\/mi><\/math>
acceleration of first mass, <\/span>a<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>24<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math>
According to Newton\u2019s second law of motion,<\/span>
F<\/mi>=<\/mo>ma<\/mi><\/math>
where <\/span>F<\/mi><\/math> is the force applied\/exerted, <\/span>m<\/mi><\/math> is the mass and <\/span>a<\/mi><\/math> is the acceleration of the body.<\/span>
For the first mass, on substituting the given values, we get<\/span>
\u21d2<\/mo> <\/mi>5<\/mn>=<\/mo>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub> <\/mi>\u00d7<\/mo>8<\/mn><\/math>
where <\/span>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/math> is the mass of the first mass.<\/span>
\u21d2<\/mo>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo>5<\/mn><\/mrow>8<\/mn><\/mrow><\/mfrac> <\/mi>kg<\/mi><\/math>
Similarly, for the first mass, on substituting the given values, we get<\/span>
\u21d2<\/mo> <\/mi>5<\/mn>=<\/mo>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub> <\/mi>\u00d7<\/mo>24<\/mn><\/math> <\/span>where <\/span>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math> is the mass of the second mass.<\/span>
\u21d2<\/mo>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo>5<\/mn><\/mrow>24<\/mn><\/mrow><\/mfrac> <\/mi>kg<\/mi><\/math>
The total mass <\/span>(<\/mo>m<\/mi>)<\/mo><\/math> if the bodies are tied together is<\/span>
\u21d2<\/mo>m<\/mi>=<\/mo>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math>
\u21d2<\/mo>m<\/mi>=<\/mo>5<\/mn><\/mrow>8<\/mn><\/mrow><\/mfrac>+<\/mo>5<\/mn><\/mrow>24<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>m<\/mi>=<\/mo>15<\/mn>+<\/mo>5<\/mn><\/mrow>24<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>m<\/mi>=<\/mo>20<\/mn><\/mrow>24<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>m<\/mi>=<\/mo>5<\/mn><\/mrow>6<\/mn><\/mrow><\/mfrac> <\/mi>kg<\/mi><\/math>
Now, the acceleration <\/span>(<\/mo>a<\/mi>)<\/mo><\/math> produced by the same force <\/span>(<\/mo>F<\/mi>)<\/mo><\/math> provided if both the masses are tied together is<\/span>
\u21d2<\/mo>a<\/mi>=<\/mo> <\/mi>F<\/mi><\/mrow>(<\/mo>m<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo> <\/mi>m<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>)<\/mo><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>a<\/mi>=<\/mo> <\/mi>5<\/mn><\/mrow>(<\/mo>5<\/mn>\/<\/mo>6<\/mn>)<\/mo><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>a<\/mi>=<\/mo>6<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math>
Hence, the acceleration is <\/span>6<\/mn> <\/mi>m<\/mi>s<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/math>.<\/span>
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