{"id":340282,"date":"2023-01-06T11:30:35","date_gmt":"2023-01-06T06:00:35","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/consider-a-planet-in-the-solar-system-which-has-a-mass-double-the-mass-of-the-earth-and-a-density-equal-to-the-average-density-of-the-earth-for-an-object-weighing-w-on-the-earth-what-will-be-the-wei\/"},"modified":"2025-06-30T11:20:40","modified_gmt":"2025-06-30T05:50:40","slug":"consider-a-planet-in-the-solar-system-which-has-a-mass-double-the-mass-of-the-earth-and-a-density-equal-to-the-average-density-of-the-earth-for-an-object-weighing-w-on-the-earth-what-will-be-the-wei","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/consider-a-planet-in-the-solar-system-which-has-a-mass-doubl\/","title":{"rendered":"Consider a planet in the solar system which has a mass double the mass of the Earth and a density equal to the average density of the Earth. For an object weighing W on the Earth, what will be the weight of the same object on the planet?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Consider a planet in the solar system which has a mass double the mass of the Earth and a density equal to the average density of the Earth. For an object weighing W on the Earth, what will be the weight of the same object on the planet?","custom_permalink":"question\/physics\/consider-a-planet-in-the-solar-system-which-has-a-mass-doubl\/"},"categories":[],"acf":{"question":"

Consider a planet in the solar system which has a mass double the mass of the Earth and a density equal to the average density of the Earth. For an object weighing <\/span>W<\/mi><\/math> on the Earth, what will be the weight of the same object on the planet?<\/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":"2<\/mn>W<\/mi><\/math>","correct":false},{"option":"3<\/mn>W<\/mi><\/math>","correct":false},{"option":"W<\/mi><\/math>","correct":false},{"option":"2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>W<\/mi><\/math> <\/span>","correct":true}],"solution":"A planet in the solar system which has a mass doubled the mass of the Earth and density equal to the average density of the Earth. An object weighing <\/span>W <\/mi><\/math>on the Earth and its weight on the planet will be <\/span>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>W<\/mi><\/math>.<\/span>
The weight of an object is the product of its mass and acceleration due to gravity. For an object, the mass is constant, and the acceleration due to gravity varies.<\/span>
The acceleration due to gravity varies as <\/span>g<\/mi><\/mrow>e<\/mi><\/mrow><\/msub>=<\/mo>G<\/mi>M<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/mrow>R<\/mi><\/mrow>e<\/mi><\/mrow>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfrac><\/math>
M<\/mi><\/mrow>e<\/mi><\/mrow><\/msub>=<\/mo><\/math> <\/span>mass of the earth<\/span>
R<\/mi><\/mrow>e<\/mi><\/mrow><\/msub>=<\/mo><\/math> radius of earth<\/span>
G<\/mi>=<\/mo><\/math> universal gravitational constant<\/span>
Given that mass of planet <\/span>M<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>2<\/mn>M<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math> <\/span>Mass of an object <\/mi>=<\/mo> Volume of the object<\/mi>\u00d7<\/mo>Density of the object<\/mi><\/math>
Mass of an object<\/mi>=<\/mo> <\/mi>4<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac>\u03c0<\/mi>r<\/mi><\/mrow>3<\/mn><\/mrow><\/msup>\u00d7<\/mo>\u03c1<\/mi><\/math>
Given that both planet and earth has same density<\/span>  <\/span>\u03c1<\/mi><\/math>
Mass of planet <\/span>M<\/mi><\/mrow>p<\/mi><\/mrow><\/msub><\/math> is equal to double times of mass of earth <\/span>M<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
\u21d2<\/mo> <\/mi>4<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac>\u03c0<\/mi>R<\/mi><\/mrow>p<\/mi><\/mrow>3<\/mn><\/mrow><\/msubsup>\u00d7<\/mo>\u03c1\u2008<\/mi>=<\/mo>\u2008<\/mi>2<\/mn>\u00d7<\/mo>4<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac>\u03c0<\/mi>R<\/mi><\/mrow>e<\/mi><\/mrow>3<\/mn><\/mrow><\/msubsup>\u00d7<\/mo>\u03c1 <\/mi><\/math>
Here <\/span>R<\/mi><\/mrow>p<\/mi><\/mrow><\/msub><\/math> and <\/span>R<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math> is the radius of planet and earth respectively.<\/span>
Then, <\/span>
\u21d2<\/mo> <\/mi>r<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>R<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
Now the acceleration due to gravity of planet <\/span>
\u21d2<\/mo> <\/mi>g<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>G<\/mi>M<\/mi><\/mrow>p<\/mi><\/mrow><\/msub><\/mrow>R<\/mi><\/mrow>p<\/mi><\/mrow>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfrac>\u2008<\/mi><\/math>
\u21d2<\/mo> <\/mi>g<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>\u2008<\/mi>G<\/mi>\u00d7<\/mo>2<\/mn>M<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/mrow>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>R<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/mrow><\/mfenced><\/mrow>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math>
\u21d2<\/mo> <\/mi>g<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>2<\/mn><\/mrow>2<\/mn><\/mrow>2<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup><\/mrow><\/mfrac>\u00d7<\/mo>g<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
\u21d2<\/mo> <\/mi>g<\/mi><\/mrow>p<\/mi><\/mrow><\/msub>=<\/mo>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>\u00d7<\/mo>g<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
The acceleration due to gravity of the planet is <\/span>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup><\/math> times of acceleration due to gravity<\/span>(<\/mo>g<\/mi><\/mrow>e<\/mi><\/mrow><\/msub>)<\/mo><\/math> of earth at the surface.<\/span>
The weight of an object on a planet is <\/span>W<\/mi><\/mrow>P<\/mi><\/mrow><\/msub>=<\/mo>m<\/mi>g<\/mi><\/mrow>p<\/mi><\/mrow><\/msub><\/math>
\u21d2<\/mo> <\/mi>W<\/mi><\/mrow>P<\/mi><\/mrow><\/msub>=<\/mo>m<\/mi>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>\u00d7<\/mo>g<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
\u21d2<\/mo> <\/mi>W<\/mi><\/mrow>p <\/mi><\/mrow><\/msub>=<\/mo>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup>\u00d7<\/mo>W<\/mi><\/mrow>e<\/mi><\/mrow><\/msub><\/math>
Hence the weight of an object on the planet is <\/span>2<\/mn><\/mrow>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/mrow><\/msup><\/math> times of weight on earth.<\/span>
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