Home
Class 12
PHYSICS
A uniform rod of length (L) and mass (M)...

A uniform rod of length (L) and mass (M) is pivoted at the centre. Its two ends are attached to two springs of equal spring constants (k). The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle (theta) in one direction and released. The frequency of oscillation is. ?
(##JMA_CHMO_C10_009_Q01##).

A

`1/(2pi) sqrt((2k)/(M))`

B

`1/(2pi)sqrt((k)/(M))`

C

`(1)/(2pi)sqrt((6k)/(M))`

D

`(1)/(2pi)sqrt((24k)/(M))`

Text Solution

Verified by Experts

The correct Answer is:
C
`x = theta(L)/(2)`
`F = - k(theta (L)/(2))`
`t_(1) = -k(theta(L)/(2))`
`t _(1) = -k(theta(L)/(2)) xx (L)/(2)`
`t_(2) = -k(theta(L)/(2)) xx (L)/(2)`
`t_("net") = -ktheta(L^(2))/(2) rArr alpha = -((kL^(2))/(2)theta) xx (12)/(mL^(2))`
`rArr - ((k6)/(m))theta rArr omega = ((k6)/(m))^(1//2) rArr f = (1)/(2pi) sqrt((6k)/(m))`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    ALLEN |Exercise MCQ s one or more than one correct answers|5 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN |Exercise Paragraph|3 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN |Exercise Exercise-05 [A]|39 Videos

  • RACE

    ALLEN |Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 Videos

  • TEST PAPER

    ALLEN |Exercise PHYSICS|4 Videos

Similar Questions

Explore conceptually related problems

Two spring of force constants k and 2k are connected to a mass as shown in figure. The frequency of oscillation of the mass is……..

Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in figure. When the mass is displaced from equilibrium position by a distance x towards right, find the restoring force.

A mass of 0.2 Kg is attached to the lower end of a massles spring of force constant 200(N)/(m) the opper end of which is fixed to a rigid support. Study the following statements.

A spring with one end attached to a mass and the other to a rigid support is stretched and released.

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is +(1/2)kx^(2) . The possible cases are.

Two identical spring of constant K are connected in series and parallel as shown in figure. A mass is suspended from them. The ratio of their frequencies of vertical oscillations will be

Two springs of spring constant k_(1)" and "k_(2) are joined in series. Hence its equivalent spring constant of the combination is…………

The thin rod shown below has mases M and length L. A force F acts at one end as shown and the rod is free to rotate about the other end in horizontal plane. Initial angular acceleration of the rod is :

Two springs are connected to a block of mass M is placed on a frictionless surface as shown in figure. If both springs have a spring constant k, the frequency of oscillation of the block is………

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O