The mass and diameter of a planet are $$4$$ times that of the earth. What will be the time period of oscillation of a pendulum on this planet, if it is a seconds pendulum on earth

Question

Infinity Learn · Accepted Answer

$$g=GMR2$$  ; M $$=$$ mass of earth; $$R=$$ radius of earth $$gplanet=G$$ $$MplanetRplanet2$$ given  $$Rp=4R$$   $$Mp=4M$$ $$gpg=GMpRp2$$×$$R2GM$$ substitute given values $$gpg=4R216R2=14$$ $$gp=g4$$      ......(1) Time period $$T=2$$$$π$$lg Time period on $$planet=Tplanet=2$$$$π$$lgplanet divide the above two equations , one by other, substitute equation (1) $$TTp=gpg=g/4g=14$$ seconds pendullum time period on earth $$=T=2$$, substitute, $$2Tp=14$$⇒$$Tp=4$$   seconds

The mass and diameter of a planet are 4 times that of the earth. What will be the time period of oscillation of a pendulum on this planet, if it is a seconds pendulum on earth

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