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A simple pendulum and a mass hanging on a spring both have a period of 1s when set into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth? 

(A) Both are shorter. 

(B) Both are the same. 

(C) Both are longer. 

(D) The period of the mass on the spring is shorter, that of the pendulum is the same. 

(E) The period of the pendulum is shorter; that of the mass on the spring is the same.

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Correct option (E) The period of the pendulum is shorter; that of the mass on the spring is the same.

A planet of the same size and twice the mass of Earth will have twice the acceleration due to gravity. The period of a mass on a spring has no dependence on g, while the period of a pendulum is inversely proportional to g.

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