A pendulum consisting of a sphere suspended from a light string is oscillating with a small angle with respect to

the vertical. The sphere is then replaced with a new sphere of the same size but greater density and is set into

oscillation with the same angle. How do the period and maximum acceleration of the new pendulum compare to

those of the original?

Period

Acceleration

a. Larger

Smaller

b. Smaller

Larger

C. The same

The same

d. The same

Smaller

Explanation:

The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”.

The period of simple pendulum is given as

T=2π√l/g

Increasing the density of the object implies that the mass has increased

Because density is mass/volume

The period is independent on the density of the object, it depends on the length of the string and the acceleration due to gravity. So the period remains the same.

2. Acceleration

The acceleration of a simple pendulum is given as

a=-gSin θ

Therefore the acceleration is independent on the density of the object, it depends on the acceleration due to gravity and the angle of displacement.

Then, the acceleration remains the same.

So the answer is Option C,

Same

Same