Question

A hollow metallic sphere filled with water is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

Solution

Correct option is

The time period will increase at first, then decrease until the sphere is empty; finally the period will be the same as that when the sphere was full of water

The length of pendulum (l) is the distance between the point of support and the centre of gravity of the sphere. The centre of gravity (CG) of a sphere is at its centre when it is empty and completely filled with water. The CG falls below the centre of the sphere as the water flows out until the sphere is half full after which the CG begins to rise. Hence the effective length of the pendulum (and hence its time period) will increase at first and decrease until the sphere is empty when it becomes equal to the time period when the sphere was full of water. 

SIMILAR QUESTIONS

Q1

Which of the following equations represents a simple harmonic motion? The displacement of the system from the equilibrium position is x at time tand α is a positive constant.

Q2

Nine tuning forks are arranged in order of increasing frequency. Each tuning fork produces 4 beats per second when sounded with either of its neighbours. If the frequency of the 9th tuning fork is twice that of the first, what is the frequency of the first tuning fork?

Q3

Figure shows the displacement-time graphs of two simple harmonic motions I and II. From the graphs it follows that the two motion I and II have

                                       

Q4

What is the phase difference between the two simple harmonic motions whose displacement-time graphs are shown in figure?

                                

Q5

 

The displacement x (in metres) of a particle in simple harmonic motion is related to time t (in seconds) as  

                            

What is the frequency of the motion? 

Q6

A simple pendulum of frequency n is taken up to a certain height above the ground and then dropped along with its support so that it falls freely under gravity. The frequency of oscillations of the falling pendulum will

Q7

A person measures the time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration of g/3, the time period of the pendulum will be

Q8

The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

Q9

A simple pendulum with a brass bob has a time period T. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is 1/8 that of brass, the time period of the same pendulum will be  

Q10

A simple pendulum of frequency f has a metal bob. If the bob is charged negatively and is allowed to oscillate with a positively charged plate placed under it, the frequency will