Explanation Explanation Given info: The distance of first star from the centre of mass is r 1 , the distance between second star from the centre of mass is r 2 and r 2 = 2 r 1 . Write the expression to calculate the time period of revolution of first star. T 1 = r 1 3 Here, T 1 is the time period of revolution of first star. r 1 is the distance of first star from the centre of mass. Thus, the time period revolution of first star is r 1 3 . Write the expression for the velocity of first star. v 1 = 2 π r 1 T 1 Here, v 1 is the velocity of first star. r 1 is the distance of first star from the centre of mass. T 1 is the time period of revolution of first star. Substitute r 1 3 for T 1 in above expression. v 1 = 2 π r 1 r 1 3 Thus, the velocity of first star is 2 π r 1 r 1 3 . Write the expression for the centripetal force acting on first star. F 1 = m 1 v 1 2 r 1 Here, F 1 is the centripetal force acting on first star. m 1 is the mass of the first star. v 1 is the velocity of first star. r 1 is the distance of first star from the centre of mass. Substitute 2 π r 1 r 1 3 for v 1 in above expression. F 1 = m 1 ( 2 π r 1 r 1 3 ) 2 r 1 = 4 m 1 π 2 r 1 2 r 1 × r 1 3 = 4 m 1 π 2 r 1 2 Thus, the centripetal force acting on first star is 4 m 1 π 2 r 1 2 . Write the expression to calculate the time period of revolution of first star. T 2 = r 2 3 Here, T 2 is the time period of revolution of second star. r 2 is the distance of second star from the centre of mass. Substitute 2 r 1 for r 2 in above expression. T 2 = ( 2 r 1 ) 3 = 8 r 1 3 Thus, the time period revolution of second star is 8 r 1 3 Write the expression for the velocity of second star. v 2 = 2 π r 2 T 2 Here, v 2 is the velocity of second star

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ISBN: 9780321976444

Author: James S. Walker

Publisher: PEARSON

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 12, Problem 76GP

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The ratio of the masses of two stars.

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Chapter 12, Problem 75GP

Chapter 12, Problem 77GP

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The ratio of the masses of two stars.

Solution Summary: The author explains that the ratio of the masses of two stars is 12. Write the expression to calculate the time period of revolution of first star

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The ratio of the masses of two stars.

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