{"id":340577,"date":"2023-01-06T11:41:53","date_gmt":"2023-01-06T06:11:53","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-weight-of-an-object-in-the-coal-mine-at-sea-level-and-at-the-top-of-the-mountain-are-respectively-w1-w2-and-w3-then-which-of-the-following-options-is-correct\/"},"modified":"2025-06-26T18:07:57","modified_gmt":"2025-06-26T12:37:57","slug":"the-weight-of-an-object-in-the-coal-mine-at-sea-level-and-at-the-top-of-the-mountain-are-respectively-w1-w2-and-w3-then-which-of-the-following-options-is-correct","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-weight-of-an-object-in-the-coal-mine-at-sea-level-and-a\/","title":{"rendered":"The weight of an object in the coal mine, at sea level and at the top of the mountain are respectively\u00a0W1, W2 and W3. Then which of the following options is correct?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The weight of an object in the coal mine, at sea level and at the top of the mountain are respectively\u00a0W1, W2 and W3. Then which of the following options is correct?","custom_permalink":"question\/physics\/the-weight-of-an-object-in-the-coal-mine-at-sea-level-and-a\/"},"categories":[],"acf":{"question":"

The weight of an object in the coal mine, at sea level and at the top of the mountain are respectively<\/span> W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/math>, <\/span>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math> and <\/span>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>. Then which of the following options is correct?<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>><\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>","correct":true},{"option":"W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>","correct":false},{"option":"W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><<\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>","correct":false},{"option":"W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>><\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>><\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>","correct":false}],"solution":"The ratio of weights of an object in the coal mine, at sea level and at the top of the mountain are <\/span>W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>><\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>.<\/span>
Weight of an object is a product of its mass and acceleration due to gravity. For every object mass is constant and the value of <\/span>g<\/mi><\/math> changes according to its height or depth.<\/span>
The variation of g at depth <\/span>d<\/mi><\/math> is <\/span>g<\/mi><\/mrow>d<\/mi><\/mrow><\/msub>\u2008<\/mi>=<\/mo>\u2008g<\/mi>1<\/mn>-<\/mo>d<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/mrow><\/mfenced><\/math>
g<\/mi><\/math> is the acceleration due to gravity at the surface of earth = <\/span>9<\/mn>.<\/mo>8<\/mn>\u2008m<\/mi>\/<\/mo>s<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
R<\/mi><\/math> = radius of earth<\/span>
The variation of g is at height <\/span>h<\/mi><\/math> is <\/span>g<\/mi><\/mrow>h<\/mi><\/mrow><\/msub>\u2008<\/mi>=<\/mo>\u2008g<\/mi>1<\/mn>-<\/mo>2<\/mn>h<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/mrow><\/mfenced><\/math>
For a coal mine at depth <\/span>d<\/mi><\/math> and at sea level, and at a height <\/span>h<\/mi><\/math> for a mountain, the ratio of weights is<\/span>
W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>:<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>:<\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
m<\/mi>g<\/mi><\/mrow>d<\/mi><\/mrow><\/msub>\u2008<\/mi>:<\/mo>\u2008mg\u2008<\/mi>:<\/mo>\u2008m<\/mi>g<\/mi><\/mrow>h<\/mi><\/mrow><\/msub><\/math>
mg<\/mi>1<\/mn>-<\/mo>d<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/mrow><\/mfenced>\u2008<\/mi>:<\/mo>\u2008mg\u2008<\/mi>:<\/mo>\u2008mg<\/mi>1<\/mn>-<\/mo>2<\/mn>h<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/mrow><\/mfenced><\/math>
Hence the ratio is, <\/span>W<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><<\/mo>W<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>><\/mo>W<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
 <\/span>","subject":""},"yoast_head":"\nThe weight of an object in the coal mine, at sea level and at the top of the mountain are respectively\u00a0W1, W2 and W3. Then which of the following options is correct? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The weight of an object in the coal mine, at sea level and at the top of the mountain are respectively\u00a0W1, W2 and W3. 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