JEE PHYSICS MCQ: OSCILLATIONS

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A solid sphere of radius

R

and density

\rho

is attached to one end of a massless spring of force constant

k

. The other end of the spring is connected to another solid sphere of radius

R

and density

3 \rho

. The complete arrangement is placed in a liquid of density

2 \rho

and is allowed to reach equilibrium. The correct statement is

View answer and explanation

Correct option: A

net elongation of spring is

\frac{4 \pi R^3 \rho g}{3 k}

and the light sphere is completely submerged

Option A (net elongation of spring is

\frac{{4 \pi R^3 \rho g}}{{3 k}}

and the light sphere is completely submerged) is correct because the buoyant force and weight balance out, leading to a specific spring elongation and complete submersion of the lighter sphere.

More Questions from OSCILLATIONS

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Assertion: A particle executing simple harmonic motion comes to rest at the extreme positions.

Reason: The resultant force on the particle is zero at these positions. A particle is subjected simultaneously to two SHM’s one along the

x

-axis and the other along the

y

-axis. The two vibrations are in phase and have unequal amplitudes. The particle will execute A particle is executing SHM with amplitude

a

. When the PE of a particle is one-fourth of its maximum value during the oscillation, its displacement from the equilibrium position will be The displacement, velocity and acceleration in a simple harmonic motion are related as the Assertion: Angular velocity of earth around sun is lesser than the angular velocity of moon about earth.
Reason: Time taken by moon revolve around earth is less than time taken by earth to revolve around sun. A particle is executing

SHM

. At a displacement

{y_1}

its potential energy is

{U_1}

and at a displacement

{y_2}

its potential energy is

{U_2}

. The potential energy of the particle at displacement

\left( {{y_1} + {y_2}} \right)