{"id":249036,"date":"2022-09-10T09:48:52","date_gmt":"2022-09-10T04:18:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-object-flying-in-air-with-velocity-20i-25j-12k-suddenly-breaks-in-two-pieces-whose-masses-are-in-the-ratio-1-5-the-smaller-mass-flies-off-with-a-velocity\/"},"modified":"2022-12-14T11:37:28","modified_gmt":"2022-12-14T06:07:28","slug":"question-physics-an-object-flying-in-air-with-velocity20i25j-12ks","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-object-flying-in-air-with-velocity20i25j-12ks\/","title":{"rendered":"An object flying in air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0–\u00a012k^)\u00a0suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity\u00a0(100i^+\u00a035j^+\u00a08k^). The velocity of the larger piece will be"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"an object flying in air with velocity 20i 25j","_yoast_wpseo_title":"An object flying in air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0-\u00a012k^)","_yoast_wpseo_metadesc":"An object flying in the air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0-\u00a012k^)\u00a0suddenly breaks into two pieces whose masses are in the ratio 1: 5.","custom_permalink":"question\/physics\/an-object-flying-in-air-with-velocity20i25j-12ks\/"},"categories":[],"acf":{"question":"

An object flying in air with velocity (<\/mo>20<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>25<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>12<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo><\/math> suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (<\/mo>100<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>35<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>8<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo><\/math>. The velocity of the larger piece will be<\/p>","options":[{"option":"

4<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>23<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>16<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>","correct":true},{"option":"

-<\/mo>100<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>35<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>8<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>","correct":false},{"option":"

20<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>15<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>80<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>","correct":false},{"option":"

-<\/mo>20<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>15<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>80<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo><\/math><\/p>","correct":false}],"solution":"

Let m be the mass of an object flying with velocity v in air. When it gets split into two pieces of masses in ratio 1 : 5, the mass of smaller piece is m\/6 and of bigger piece is 5<\/mn>m<\/mi><\/mrow>6<\/mn><\/mfrac>.<\/mo><\/math><\/p>

This situation can be interpreted diagrammatically as below.<\/p>

<\/figure>

As, the object breaks in two pieces, so the momentum of the system will remains conserved, i.e. the total momentum (before breaking) = total momentum (after breaking)<\/p>

                     m<\/mi>v<\/mi>=<\/mo>m<\/mi>6<\/mn><\/mfrac>v<\/mi>1<\/mn><\/msub>+<\/mo>5<\/mn>m<\/mi><\/mrow>6<\/mn><\/mfrac>v<\/mi>2<\/mn><\/msub>\u21d2<\/mo>v<\/mi>=<\/mo>v<\/mi>1<\/mn><\/msub>6<\/mn><\/mfrac>+<\/mo>5<\/mn>v<\/mi>2<\/mn><\/msub><\/mrow>6<\/mn><\/mfrac><\/math><\/p>

Given,  v<\/mi>=<\/mo> <\/mo>20<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>25<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>12<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>

and      v<\/mi>1<\/mn><\/msub> <\/mo>=<\/mo> <\/mo>100<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>35<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>8<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>

Putting these values in Eq. (i), we get<\/p>

(<\/mo>20<\/mn>i<\/mi>^<\/mo><\/mover>+<\/mo>25<\/mn>j<\/mi>^<\/mo><\/mover>-<\/mo>12<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo>=<\/mo>(<\/mo>100<\/mn>i<\/mi>^<\/mo><\/mover>+<\/mo>35<\/mn>j<\/mi>^<\/mo><\/mover>+<\/mo>8<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo><\/mrow>6<\/mn><\/mfrac>+<\/mo>5<\/mn>v<\/mi>2<\/mn><\/msub><\/mrow>6<\/mn><\/mfrac><\/math><\/p>

\u21d2<\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>  <\/mo>(<\/mo>120<\/mn>i<\/mi>^<\/mo><\/mover>+<\/mo>150<\/mn>j<\/mi>^<\/mo><\/mover>-<\/mo>72<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo>=<\/mo>(<\/mo>100<\/mn>i<\/mi>^<\/mo><\/mover>+<\/mo>35<\/mn>j<\/mi>^<\/mo><\/mover>+<\/mo>8<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo>+<\/mo>5<\/mn>v<\/mi>2<\/mn><\/msub><\/math><\/p>

\u21d2<\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>v<\/mi>2<\/mn><\/msub>=<\/mo>1<\/mn>5<\/mn><\/mfrac>(<\/mo>20<\/mn>i<\/mi>^<\/mo><\/mover>+<\/mo>115<\/mn>j<\/mi>^<\/mo><\/mover>-<\/mo>80<\/mn>k<\/mi>^<\/mo><\/mover>)<\/mo><\/math><\/p>

                   =<\/mo>4<\/mn>i<\/mi>^<\/mo><\/mover> <\/mo>+<\/mo> <\/mo>23<\/mn>j<\/mi>^<\/mo><\/mover> <\/mo>-<\/mo> <\/mo>16<\/mn>k<\/mi>^<\/mo><\/mover><\/math><\/p>","subject":""},"yoast_head":"\nAn object flying in air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0-\u00a012k^)<\/title>\n<meta name=\"description\" content=\"An object flying in the air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0-\u00a012k^)\u00a0suddenly breaks into two pieces whose masses are in the ratio 1: 5.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-object-flying-in-air-with-velocity20i25j-12ks\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An object flying in air with velocity\u00a0(20i^\u00a0+\u00a025j^\u00a0-\u00a012k^)\" 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