Question

A spring has a natural length of 50 cm and a force constant of  A body of mass 10 kg is suspended from it and the spring is stretched. If the body is pulled down further stretching the spring to a length of 58 cm and released, it executes simple harmonic motion. What is the net force on the body when it is at its lowermost position of its oscillation? Take g = 10 ms –2.

Solution

Correct option is

60 N

 

The extension produced in the string when the mass is suspended from it is

                        

Thus the equilibrium position of the mass corresponds to a position when the length of the spring = 50 + 5 = 55 cm. the lowermost position of the mass corresponds to a position when the length of the spring is 58 cm, i.e. when the spring is stretched by 58 – 50 = 8 cm. This position is (8 – 5) = 3 cm below the equilibrium position. At the equilibrium position, no net force acts on the body because the downward force mg is balanced by the restoring ky of the spring. Therefore, at the lowermost position, the force exerted by the spring on the mass is  

F = force constant × extension below the equilibrium position  

   

SIMILAR QUESTIONS

Q1

A tuning fork produces 4 beta per second when sounded with sonometer of vibrating length 48cm. It produces 4 beats per second also when the vibrating length is 50cm. What is the frequency of the tuning fork?

Q2

 

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as 

                         

The magnitude of the maximum acceleration of the particle is 

Q3

A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

Q4

A body executing linear simple harmonic motion has a velocity of 3 cms–1when its displacement is 4 cm and a velocity of 4 cms–1 when its displacement is 3 cm. what is the amplitude of oscillation?  

Q5

A particle is executing linear simple harmonic motion of amplitude A. what fraction of the total energy is kinetic when the displacement is half the amplitude?

Q6

Two identical strings of a stringed  musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the string were in unison?

Q7

A horizontal platform is executing simple harmonic motion in the vertical direction of frequency v. A block of mass m is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?

Q8

A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take g = 10 ms–2.  

Q9

A spring of negligible mass having a force constant k extends by an amount y when a mass m is hung from it. The mass is pulled down a little and released. The system begins to execute simple harmonic motion of amplitude A and angular frequency ω. The total energy of the mass-spring system will be

Q10

A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. When the turntable is rotated an angular frequency of 10 rad s–1, the length of the spring becomes 40 cm. what is the force constant of the spring?