A Solid Brass Sphere Is Hung From A Spring Whose Mass Is Negligible Compared To That Of The Sphere. The Sphere Is Set Into Vertical Oscillations And Its Time Period Is Found To Be T. The Sphere Is Now Completely Immersed In A Liquid Whose Density Is 1/8th that Of Brass. The Time Period Of Vertical Oscillations With The Sphere Always Remaining Immersed In The Liquid Will Be Equal To

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Question

A solid brass sphere is hung from a spring whose mass is negligible compared to that of the sphere. The sphere is set into vertical oscillations and its time period is found to be T. The sphere is now completely immersed in a liquid whose density is 1/8th that of brass. The time period of vertical oscillations with the sphere always remaining immersed in the liquid will be equal to

Solution

Correct option is

T

The time period of the vertical oscillations depends on the mass (m) of the sphere and the force constant (k) of the sphere. Since neither m nor k will change when the sphere is immersed in a liquid, the time period will remain unchanged.

Testing

SIMILAR QUESTIONS

Q1

 

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? 

Q2

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

Q3

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

Q4

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

Q5

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?

Q6

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  

Q7

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 

Q8

A wooden block is suspended from a spring. Its period for vertical oscillations is T. In a second experiment the same apparatus is laid on a horizontal frictionless table with the free end of the spring fixed to a nail on the table. The block is pulled a little so as to stretch the spring and then released. The mass will   

Q9

The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 parts of hydrogen and 2 parts of oxygen at STP will be.

Q10

A heavy metal sphere is suspended from a spring. When pulled down a little and released, it oscillates up and down with a frequency f. If it is taken to the moon (where the acceleration due to gravity is one-sixth that on earth) the frequency of vertical oscillation will