{"id":261126,"date":"2022-09-10T12:34:46","date_gmt":"2022-09-10T07:04:46","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-value-of-gravitation-constant-is-g6-67x10-11-n%c2%b7m2-kg2-in-si-units-convert-it-into-cgs-system-of-units\/"},"modified":"2022-09-10T12:34:46","modified_gmt":"2022-09-10T07:04:46","slug":"the-value-of-gravitation-constant-is-g6-67x10-11-n%c2%b7m2-kg2-in-si-units-convert-it-into-cgs-system-of-units","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-value-of-gravitation-constant-isg66710-11nm2kg2i\/","title":{"rendered":"The value of gravitation constant is\u00a0G=6.67\u00d710-11\u00a0N\u00b7m2\/kg2\u00a0in SI units. Convert it into\u00a0CGS\u00a0system of units."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The value of gravitation constant is\u00a0G=6.67\u00d710-11\u00a0N\u00b7m2\/kg2\u00a0in SI units. Convert it into\u00a0CGS\u00a0system of units.","custom_permalink":"question\/physics\/the-value-of-gravitation-constant-isg66710-11nm2kg2i\/"},"categories":[],"acf":{"question":"

The value of gravitation constant is G<\/mi>=<\/mo>6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>11<\/mn><\/mrow><\/msup> <\/mo>N<\/mi>\u00b7<\/mo>m<\/mi>2<\/mn><\/msup>\/<\/mo>kg<\/mi>2<\/mn><\/msup><\/math> in SI units. Convert it into C<\/mi>G<\/mi>S<\/mi><\/math> system of units.<\/p>","options":[{"option":"

6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>8<\/mn><\/mrow><\/msup> dyne <\/mtext>cm<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup>\/<\/mo>g<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false},{"option":"

6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>8<\/mn><\/msup> dyne <\/mtext>cm<\/mi>2<\/mn><\/msup>\/<\/mo>g<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false},{"option":"

6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>8<\/mn><\/mrow><\/msup> dyne <\/mtext>cm<\/mi>2<\/mn><\/msup>\/<\/mo>g<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":true},{"option":"

6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>8<\/mn><\/mrow><\/msup> dyne <\/mtext>cm<\/mi>2<\/mn><\/msup>\/<\/mo>g<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math><\/p>","correct":false}],"solution":"

The dimensional formula of G is <\/span>M<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup> <\/mo>L<\/mi><\/mrow>3<\/mn><\/msup> <\/mo>T<\/mi><\/mrow>-<\/mo>2<\/mn><\/mrow><\/msup><\/mrow><\/mfenced><\/math>. <\/p>

Using Eq. <\/p>

n<\/mi>1<\/mn><\/msub>M<\/mi>1<\/mn>-<\/mo>1<\/mn><\/mrow><\/msubsup> <\/mo>L<\/mi><\/mrow>1<\/mn>3<\/mn><\/msubsup> <\/mo>T<\/mi><\/mrow>1<\/mn>-<\/mo>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfenced>=<\/mo>n<\/mi>2<\/mn><\/msub>M<\/mi>2<\/mn>-<\/mo>1<\/mn><\/mrow><\/msubsup> <\/mo>L<\/mi><\/mrow>2<\/mn>3<\/mn><\/msubsup> <\/mo>T<\/mi><\/mrow>2<\/mn>-<\/mo>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfenced>n<\/mi>2<\/mn><\/msub>=<\/mo>n<\/mi>1<\/mn><\/msub>M<\/mi>1<\/mn><\/msub>M<\/mi>2<\/mn><\/msub><\/mfrac><\/mfenced>-<\/mo>1<\/mn><\/mrow><\/msup>L<\/mi>1<\/mn><\/msub> <\/mo>L<\/mi><\/mrow>2<\/mn><\/msub><\/mfrac><\/mfenced>3<\/mn><\/msup>T<\/mi>1<\/mn><\/msub> <\/mo>T<\/mi><\/mrow>2<\/mn><\/msub><\/mfrac><\/mfenced>-<\/mo>2<\/mn><\/mrow><\/msup><\/math><\/p>

Here, n<\/mi>1<\/mn><\/msub>=<\/mo>6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>11<\/mn><\/mrow><\/msup>M<\/mi>1<\/mn><\/msub>=<\/mo>1<\/mn> <\/mo>kg<\/mi>,<\/mo>M<\/mi>2<\/mn><\/msub>=<\/mo>1<\/mn> <\/mo>g<\/mi>=<\/mo>10<\/mn>-<\/mo>3<\/mn><\/mrow><\/msup> <\/mo>kg<\/mi>,<\/mo>L<\/mi>1<\/mn><\/msub>=<\/mo>1<\/mn> <\/mo>m<\/mi>,<\/mo>L<\/mi>2<\/mn><\/msub>=<\/mo>1<\/mn> <\/mo>cm<\/mi>=<\/mo>10<\/mn>-<\/mo>2<\/mn><\/mrow><\/msup> <\/mo>m<\/mi>,<\/mo>T<\/mi>1<\/mn><\/msub>=<\/mo>T<\/mi>2<\/mn><\/msub>=<\/mo>1<\/mn> <\/mo>s<\/mi><\/math><\/p>

Substituting in the above equation, we get<\/p>

n<\/mi>2<\/mn><\/msub>=<\/mo>6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>11<\/mn><\/mrow><\/msup>1<\/mn> <\/mo>kg<\/mi><\/mrow>10<\/mn>-<\/mo>3<\/mn><\/mrow><\/msup> <\/mo>kg<\/mi><\/mrow><\/mfrac><\/mfenced>-<\/mo>1<\/mn><\/mrow><\/msup>1<\/mn> <\/mo>m<\/mi><\/mrow>10<\/mn>-<\/mo>2<\/mn><\/mrow><\/msup> <\/mo>m<\/mi><\/mrow><\/mfrac><\/mfenced>3<\/mn><\/msup>1<\/mn> <\/mo>s<\/mi><\/mrow>1<\/mn> <\/mo>s<\/mi><\/mrow><\/mfrac><\/mfenced>-<\/mo>2<\/mn><\/mrow><\/msup><\/math><\/p>

or, n<\/mi>2<\/mn><\/msub>=<\/mo>6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>8<\/mn><\/mrow><\/msup><\/math><\/p>

Thus value of G in CGS system of units is <\/span>6<\/mn>.<\/mo>67<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>8<\/mn><\/mrow><\/msup> dyne <\/mtext>cm<\/mi>2<\/mn><\/msup>\/<\/mo>g<\/mi>2<\/mn><\/msup><\/math>.<\/p>","subject":""},"yoast_head":"\nThe value of gravitation constant is\u00a0G=6.67\u00d710-11\u00a0N\u00b7m2\/kg2\u00a0in SI units. Convert it into\u00a0CGS\u00a0system of units. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The value of gravitation constant is\u00a0G=6.67\u00d710-11\u00a0N\u00b7m2\/kg2\u00a0in SI units. 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