Question

A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in a liquid of density d. When pushed down a little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.

Solution

Correct option is

 

The dimensions of 

                      

SIMILAR QUESTIONS

Q1

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

Q2

 

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?

Q3

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.

Q4

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 

Q5

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.

Q6

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

Q7

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 

Q8

 

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   

Q9

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

Q10

 

When a wave travels in a medium, the particle displacements are given by

                   

Where y and x are in meters and t in seconds. The wavelength of the wave is