Question

 

Two masses m1 and m2 are suspended together by a massless spring of force constant k (see fig). When the masses are in equilibrium, mass m1 is removed without disturbing the system. The angular frequency of oscillation of mass m2 is   

Solution

Correct option is

Let x1 be the extension produced in the spring when it is loaded with massm2 alone and x2 be the further extension when mass m1 is added to massm2 so that x1 + x2 is the total extension produced by . Thus we have, 

                                              

For equilibrium state of m2  

                             

For equilibrium state of (m1 + m2)

                           

When the mass m1 is removed, the mass m2 will move upwards under the unbalanced force = m1 g. Hence

Restoring force (F) on m2 = – m1 g   

Subtracting (i) and (ii) we have

                           

Hence, Restoring force on m2 = – kx2      

 

SIMILAR QUESTIONS

Q1

A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolley is displaced from its equilibrium position by a distance x and released. The trolley executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

                                                         

Q2

Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. figure (b) shows the same spring with both ends free and a mass m fixed at each free end. Each of the spring is stretched by the same force F. the mass is case (a) and the masses in case (b) are then released.

                                                                  

Which of the following statements is/are true? 

Q3

A simple pendulum of bob mass m is oscillating with an angular amplitudeαm (in radius). The maximum tension in the string is

Q4

 

A particle is executing simple harmonic motion. Its displacement is given by   

                       

where x is in cm and t in seconds. How long will the particle take to move from the position of equilibrium to the position of maximum displacement?

Q5

A simple pendulum is moving simple harmonically with a period of 6 s between two extreme position B and C about a point O. if the angular distance between B and C is 10 cm, how long will the pendulum take to move from position C to a position D exactly midway between O and C.

Q6

A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is 2.5 cm. What must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10 ms –2 

Q7

A spring with no mass attached to it hangs from a rigid support. A mass mis now hung on the lower end to the spring. The mass is supported on a platform so that the spring remains relaxed. The supporting platform is then suddenly removed and the mass begins to oscillate. The lowest position of the mass during the oscillation is 5 cm below the place where it was resting on the platform. What is the angular frequency of oscillation? Take g = 10 ms–2.

Q8

When a mass m is hung from the lower of a spring of negligible mass, an extension x is produced in the spring. The mass is set into vertical oscillations. The time period of oscillation is

Q9

A small spherical steel ball is placed a little away from the centre of a large concave mirror of radius of curvature R = 2.5 m. The ball is then released. What is the time period of the motion? Neglect friction and take 

Q10

A mass m is suspended at the end of a massless wire of length L and cross-sectional area A. If Y is the Young’s modulus of the material of the wire, the frequency of oscillations along the vertical line is given by