{"id":261193,"date":"2022-09-10T12:35:33","date_gmt":"2022-09-10T07:05:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-thin-uniform-circular-disc-of-mass-m-and-radius-r-is-rotating-in-a-horizontal-plane-about-an-axis-passing-through-its-centre-and-perpendicular-to-its-plane-with-angular-velocity-%cf%89-another\/"},"modified":"2022-09-10T12:35:33","modified_gmt":"2022-09-10T07:05:33","slug":"a-thin-uniform-circular-disc-of-mass-m-and-radius-r-is-rotating-in-a-horizontal-plane-about-an-axis-passing-through-its-centre-and-perpendicular-to-its-plane-with-angular-velocity-%cf%89-another","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-thin-uniform-circular-disc-of-mass-m-and-radius-r-is-rotat\/","title":{"rendered":"A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity\u00a0\u03c9: Another disc of same dimensions\u00a0but of mass M\/4 is placed gently on the first disc co-axially. The angular velocity\u00a0\u03c9’of the system is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity\u00a0\u03c9: Another disc of same dimensions\u00a0but of mass M\/4 is placed gently on the first disc co-axially. The angular velocity\u00a0\u03c9'of the system is","custom_permalink":"question\/physics\/a-thin-uniform-circular-disc-of-mass-m-and-radius-r-is-rotat\/"},"categories":[],"acf":{"question":"

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity \u03c9<\/mi><\/math>: Another disc of same dimensions <\/p>
<\/figure>

but of mass M\/4 is placed gently on the first disc co-axially. The angular velocity \u03c9<\/mi><\/math>'of the system is<\/p>","options":[{"option":"

2<\/mn><\/msqrt>\u03c9<\/mi><\/math><\/p>","correct":false},{"option":"

(<\/mo>4<\/mn>\/<\/mo>5<\/mn>)<\/mo>\u03c9<\/mi><\/math><\/p>","correct":true},{"option":"

 (3\/4) <\/mtext>\u03c9<\/mi><\/math><\/p>","correct":false},{"option":"

(<\/mo>1<\/mn>\/<\/mo>3<\/mn>)<\/mo>\u03c9<\/mi><\/math><\/p>","correct":false}],"solution":"

Applying the law of conservation of angular momentum, we have
1<\/mn>2<\/mn><\/mfrac>MR<\/mi>2<\/mn><\/msup><\/mrow><\/mfenced>\u03c9<\/mi>=<\/mo>1<\/mn>2<\/mn><\/mfrac>MR<\/mi>2<\/mn><\/msup>+<\/mo>1<\/mn>2<\/mn><\/mfrac>M<\/mi>4<\/mn><\/mfrac><\/mfenced>R<\/mi>2<\/mn><\/msup><\/mrow><\/mfenced>\u03c9<\/mi>\u2032<\/mi><\/msup><\/mtd><\/mtr>\u03c9<\/mi>=<\/mo>5<\/mn>4<\/mn><\/mfrac>\u03c9<\/mi>\u2032<\/mi><\/msup> <\/mspace> or <\/mtext> <\/mspace>\u03c9<\/mi>\u2032<\/mi><\/msup>=<\/mo>4<\/mn>5<\/mn><\/mfrac><\/mfenced>\u03c9<\/mi><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"\nA thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity\u00a0\u03c9: Another disc of same dimensions\u00a0but of mass M\/4 is placed gently on the first disc co-axially. The angular velocity\u00a0\u03c9'of the system is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity\u00a0\u03c9: Another disc of same dimensions\u00a0but of mass M\/4 is placed gently on the first disc co-axially. 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The angular velocity\u00a0\u03c9'of the system is - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity\u00a0\u03c9: Another disc of same dimensions\u00a0but of mass M\/4 is placed gently on the first disc co-axially. 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