{"id":544311,"date":"2023-04-23T10:36:03","date_gmt":"2023-04-23T05:06:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-stone-of-mass-50-grams-is-attached-to-one-end-of-a-string-of-length-1-meter-the-maximum-tension-in-the-string-can-withstand-is\/"},"modified":"2025-06-20T15:17:31","modified_gmt":"2025-06-20T09:47:31","slug":"a-stone-of-mass-50-grams-is-attached-to-one-end-of-a-string-of-length-1-meter-the-maximum-tension-in-the-string-can-withstand-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-stone-of-mass-50-grams-is-attached-to-one-end-of-a-s\/","title":{"rendered":"Given that a stone with a mass of 50 grams is attached to a 1-meter string and spun in a horizontal circle, if the maximum tension the string can withstand is 200N, what is the maximum speed at which the stone can be rotated without breaking the string?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\u00a0A stone\u00a0 of mass\u00a0 50 grams\u00a0 is attached\u00a0 to one end\u00a0 of\u00a0 a string\u00a0 of length\u00a0 1 meter The maximum tension\u00a0 in the string\u00a0 can withstand\u00a0 is 200N . The\u00a0 stone\u00a0 is rotated\u00a0 uniformly in\u00a0 a horizontal\u00a0 circle. Read\u00a0 the\u00a0 above passage\u00a0 and answer\u00a0 the following\u00a0 questions.","custom_permalink":"question\/physics\/a-stone-of-mass-50-grams-is-attached-to-one-end-of-a-s\/"},"categories":[],"acf":{"question":"

 A stone  of mass  50 grams  is attached  to one end  of  a string  of length  1 meter The maximum tension  in the string  can withstand  is 200N . The  stone  is rotated  uniformly in  a horizontal  circle. Read  the  above passage  and answer  the following  questions.<\/p>","options":null,"solution":"

\r\n
\r\n
\r\n\r\nTo find the maximum speed at which the stone can be rotated without breaking the string, we can use the formula for the centripetal force, which must be equal to or less than the maximum tension the string can withstand. The formula for centripetal force\r\n\r\nF<\/mi>c<\/mi><\/msub><\/mrow>F_c<\/annotation><\/semantics><\/math>F<\/span>c<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is:\r\n\r\n \r\n\r\nF<\/mi>c<\/mi><\/msub>=<\/mo>m<\/mi>v<\/mi>2<\/mn><\/msup><\/mrow>r<\/mi><\/mfrac><\/mrow>F_c = \\frac{m v^2}{r}<\/annotation><\/semantics><\/math>F<\/span>c<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>r<\/span>m<\/span>v<\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Where:\r\n
    \r\n \t
  • \r\nm<\/mi><\/mrow>m<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nm<\/span><\/span><\/span><\/span> is the mass of the stone,<\/li>\r\n \t
  • \r\nv<\/mi><\/mrow>v<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nv<\/span><\/span><\/span><\/span> is the velocity (speed) of the stone,<\/li>\r\n \t
  • \r\nr<\/mi><\/mrow>r<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nr<\/span><\/span><\/span><\/span> is the radius of the circle (length of the string).<\/li>\r\n<\/ul>\r\nGiven:\r\n
      \r\n \t
    • \r\nm<\/mi>=<\/mo>50<\/mn><\/mrow>m = 50<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nm<\/span>=<\/span><\/span>50<\/span><\/span><\/span><\/span> grams = 0.05 kg (since 1<\/mn>\u00a0gram<\/mtext>=<\/mo>0.001<\/mn>\u00a0kg<\/mtext><\/mrow>1 \\text{ gram} = 0.001 \\text{ kg}<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\n1<\/span>\u00a0gram<\/span><\/span>=<\/span><\/span>0.001<\/span>\u00a0kg<\/span><\/span><\/span><\/span><\/span>),<\/li>\r\n \t
    • \r\nr<\/mi>=<\/mo>1<\/mn><\/mrow>r = 1<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nr<\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span> meter,<\/li>\r\n \t
    • The maximum tension (maximum force \r\nF<\/mi>c<\/mi><\/msub><\/mrow>F_c<\/annotation><\/semantics><\/math><\/span><\/span><\/span> \r\n\r\nF<\/span>c<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) the string can withstand = 200 N.<\/li>\r\n<\/ul>\r\nWe rearrange the formula to solve for\r\n\r\nv<\/mi><\/mrow>v<\/annotation><\/semantics><\/math>v<\/span><\/span><\/span>:\r\n\r\n \r\n\r\nv<\/mi>=<\/mo>F<\/mi>c<\/mi><\/msub>\u22c5<\/mo>r<\/mi><\/mrow>m<\/mi><\/mfrac><\/msqrt><\/mrow>v = \\sqrt{\\frac{F_c \\cdot r}{m}}<\/annotation><\/semantics><\/math>v<\/span>=<\/span><\/span>m<\/span>F<\/span>c<\/span><\/span>\u200b<\/span><\/span>\u22c5<\/span>r<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span>Substituting the given values:\r\n\r\n \r\n\r\nv<\/mi>=<\/mo>200<\/mn>\u22c5<\/mo>1<\/mn><\/mrow>0.05<\/mn><\/mfrac><\/msqrt><\/mrow>v = \\sqrt{\\frac{200 \\cdot 1}{0.05}}<\/annotation><\/semantics><\/math>v<\/span>=<\/span><\/span>0.05200\u22c5<\/span>1\u200b<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span>Let's calculate that.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n
      \r\n
      \r\n\r\nThe maximum speed at which the stone can be rotated without breaking the string is approximately\r\n\r\n63.25<\/mn>\u2009<\/mtext>m\/s<\/mtext><\/mrow>63.25 \\, \\text{m\/s}<\/annotation><\/semantics><\/math>63.25<\/span>m\/s<\/span><\/span><\/span><\/span>. \u200b\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","subject":"Physics"},"yoast_head":"\nGiven that a stone with a mass of 50 grams is attached to a 1-meter string and spun in a horizontal circle, if the maximum tension the string can withstand is 200N, what is the maximum speed at which the stone can be rotated without breaking the string? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"\u00a0A stone\u00a0 of mass\u00a0 50 grams\u00a0 is attached\u00a0 to one end\u00a0 of\u00a0 a string\u00a0 of length\u00a0 1 meter The maximum tension\u00a0 in the string\u00a0 can withstand\u00a0 is 200N . The\u00a0 stone\u00a0 is rotated\u00a0 uniformly in\u00a0 a horizontal\u00a0 circle. 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