Question

One end a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period given by

Solution

Correct option is

 

If the wire extends by an amount when a force F is applied to it, then

                                      

Thus the force constant of the wire is k. If K is the force constant of the spring, then the force constant of the series combination of the wire and the spring is given by 

                         

the time period of the combination is  

               

Using (i) in  (ii) we find that 

SIMILAR QUESTIONS

Q1

The difference between the apparent frequencies of a source of sound as perceived by an observer during its approach and recession is 2% of the actual frequency of the source. If the speed of sound in air is 300 ms–1, the speed of the source is

Q2

A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in the tension of the string produces fewer beats per second than before?

Q3

A train blowing its whistle moves with a constant velocity u away from the observer on the ground. The ratio of the actual frequency of the whistle to that measured by the observer is found to be 1.2. If the train is at rest and the observer moves away from it at the same velocity, the ratio would be given by

Q4

The intensity of sound gets reduced by 20% on passing through a slab. The reduction in intensity on passage through two consecutive slabs is

Q5

 

Two sounding bodies producing progressive waves given by 

                                     

are situated very near to the ears of a person who will hear

Q6

An organ pipe P1, closed at one end vibrating in its first harmonic and another pipe P2, open at both ends vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the lengths of P1 and P2is

Q7

Two identical straight wires are stretched so to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1 andT2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension.

Q8

The time taken by a particle executing simple harmonic motion of time period T to move from the mean position to half the maximum displacement is

Q9

To raise the pitch of a stringed musical instrument, the player can

Q10

A weight is attached to the free end of a sonometer wire. Resonance occurs at a length of 40 cm of the wire with a tuning fork of frequency 512 Hz. The weight is then immersed wholly in water, the resonant length is reduced to 30 cm. The relative density of the weight is