Question

Masses $${M_A}$$ and $${M_B}$$ hanging from the ends of strings of lengths $${L_A}$$ and $${L_B}$$ are executing simple harmonic motions. If their frequencies are $${f_A} = 2{f_B},$$   then

A. $${L_A} = 2{L_B}\,{\text{and}}\,{M_A} = \frac{{{M_B}}}{2}$$
B. $${L_A} = 4{L_B}$$   regardless of masses
C. $${L_A} = \frac{{{L_B}}}{4}$$   regardless of masses  
D. $${L_A} = 2{L_B}\,{\text{and}}\,{M_A} = 2{M_B}$$
Answer :   $${L_A} = \frac{{{L_B}}}{4}$$   regardless of masses
Solution :
$$\eqalign{ & {f_A} = \frac{1}{{2\pi }}\sqrt {\frac{g}{{{L_A}}}} \,\,{\text{and}}\,\,{f_B} = \frac{{{f_A}}}{2} = \frac{1}{{2\pi }}\sqrt {\frac{g}{{{L_B}}}} \cr & \therefore \frac{{{f_A}}}{{\frac{{{f_A}}}{2}}} = \frac{1}{{2\pi }}\sqrt {\frac{g}{{{L_A}}}} \times 2\pi \sqrt {\frac{{{L_B}}}{g}} \Rightarrow 2 = \sqrt {\frac{{{L_B}}}{{{L_A}}}} \cr & \Rightarrow 4 = \frac{{{L_B}}}{{{L_A}}},\,{\text{regardless of mass}}{\text{.}} \cr} $$

Releted MCQ Question on
Oscillation and Mechanical Waves >> Simple Harmonic Motion (SHM)

Releted Question 1

Two bodies $$M$$ and $$N$$ of equal masses are suspended from two separate massless springs of spring constants $${k_1}$$ and $${k_2}$$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of $$M$$ to that of $$N$$ is

A. $$\frac{{{k_1}}}{{{k_2}}}$$
B. $$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $$
C. $$\frac{{{k_2}}}{{{k_1}}}$$
D. $$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $$
View Answer
Releted Question 2

A particle free to move along the $$x$$-axis has potential energy given by $$U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$$      for $$ - \infty \leqslant x \leqslant + \infty ,$$    where $$k$$ is a positive constant of appropriate dimensions. Then

A. at points away from the origin, the particle is in unstable equilibrium
B. for any finite nonzero value of $$x,$$ there is a force directed away from the origin
C. if its total mechanical energy is $$\frac{k}{2},$$  it has its minimum kinetic energy at the origin.
D. for small displacements from $$x = 0,$$  the motion is simple harmonic
View Answer
Releted Question 3

The period of oscillation of a simple pendulum of length $$L$$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $$\alpha ,$$ is given by

A. $$2\pi \sqrt {\frac{L}{{g\cos \alpha }}} $$
B. $$2\pi \sqrt {\frac{L}{{g\sin \alpha }}} $$
C. $$2\pi \sqrt {\frac{L}{g}} $$
D. $$2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $$
View Answer
Releted Question 4

A particle executes simple harmonic motion between $$x = - A$$  and $$x = + A.$$  The time taken for it to go from 0 to $$\frac{A}{2}$$ is $${T_1}$$ and to go from $$\frac{A}{2}$$ to $$A$$ is $${T_2.}$$ Then

A. $${T_1} < {T_2}$$
B. $${T_1} > {T_2}$$
C. $${T_1} = {T_2}$$
D. $${T_1} = 2{T_2}$$
View Answer

Practice More Releted MCQ Question on
Simple Harmonic Motion (SHM)

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Basic PhysicsUnit and MeasurementKinematicsLaws of MotionFrictionUniform Circular MotionImpulseMomentumWork Energy and PowerRotational MotionGravitationMechanical Properties of Solids and Fluids
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Modern PhysicsDual Nature of Matter and RadiationAtoms And NucleiAtoms or Nuclear Fission and FusionRadioactivityModern Physics MiscellaneousSemiconductors and Electronic Devices
Oscillation and Mechanical WavesSimple Harmonic Motion (SHM)Waves