AP Physics B & C –Free-Response Question (for practice) on Simple Pendulum

The following free response question will be useful for both AP Physics B and C aspirants:

A simple pendulum of length ℓ is set up using of a bob of mass m and a string of negligible mass. The string can withstand a maximum tension of 3mg where g is the acceleration due to gravity. The bob is pulled aside so that the string makes a small angle θ₁ with the vertical. On releasing the bob, the pendulum oscillates with period T. Now, answer the following questions:

(a) Calculate the period of oscillation when the length ℓ = 1 m, assuming that the acceleration due to gravity at the place is 10 ms^–2.

(b) If the bob of the pendulum is now immersed in a liquid of negligible viscosity and of density lower than that of the bob, how will the period be affected? Put a tick mark against the correct option:

Increased ___ Decreased ___ Unchanged ___

Give reason for your answer.

(c) The pendulum bob is taken out from liquid and is oscillated in air itself. Explain what modification you will make to halve the period of oscillation.

(d) The centre of gravity of the bob is raised through a height of 6 cm from its mean position (lowest position) when the bob is in the extreme position during its oscillation. Calculate the speed of the bob when it crosses the mean position.

(e) Calculate the maximum angle through which the string can be displaced from the vertical so that the string will not break when the pendulum oscillates.

Try to answer the above question which carries 15 points which can be distributed among the parts (a), (b), (c), (d) and (e) as 2+3+2+4+4. You can take about 17 minutes for answering the above question.

I’ll be back with a model answer for your benefit shortly.