JEE Main 2015 · 10 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then :

T^2\propto r^3

T\propto r^2

T\propto r

T\propto\sqrt r

Answer and worked solution

Official answer: C

Outside a long cylinder $g=\dfrac{2G\lambda}r$ . Setting it equal to $\omega^2r$ :
$\omega^2=\frac{2G\lambda}{r^2}\implies T\propto r.$

Topics:Satellites and orbital motion Gravitational field and potential

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JEE Main 2015 · 10 Apr · Shift 1, Physics question 7