There is an isolated planet having mass 2 M and radius 2 R , where M and R are the mass and radius of the earth. A simple pendulum having mass m and length 2 R is made to small oscillations on the planet. The time period of SHM of pendulum

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There is an isolated planet having mass 2 M and radius 2 R , where M and R are the mass and radius of the earth. A simple pendulum having mass m and length 2 R is made to small oscillations on the planet. The time period of SHM of pendulum is (0.7 ~K +0.5) seconds. Find the value of K. (take =3.00, ~g =10 ~m / s ^2, 2 =1.41 )

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Correct answer: 9

aligned & g= G M R^2 & g^ = G 2 m 4 R^2 & g^ = g 2 & F=-m g^ & F=- m g 2 2 aligned As is much small aligned & ma =- mg 2 2 & a =- g & a =- g x 2 R aligned aligned & = g 2 R f ~T & =2 2 R g ~T & =2 3.14 2 6400 10^3 10 = & 2 3 800 1.41 ~T & =6768 ~s . aligned

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