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Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

A bob is suspended from an ideal string of length $l$. Now it is pulled to a side through $60^{o}$ to vertical and rotates along a horizontal circle. Then its period of revolution is

  1. $ 2\pi \sqrt{ l/g }$
  2. $ \pi \sqrt{ l/2g }$
  3. $\pi\sqrt{ 2l/g }$
  4. $\pi\sqrt{ l/g }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a conical pendulum, the period is T = 2*pi*sqrt(h/g), where h = l*cos(theta). For theta = 60 degrees, cos(60) = 1/2, so h = l/2. Thus, T = 2*pi*sqrt(l/(2g)) = pi*sqrt(2l/g).

Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

Write the torque equation for the bob of a pendulum if it makes an angle of $\theta$ with the vertical and I is the moment of inertia of the bob w.r.t the point of suspension

  1. $I \dfrac{d^2 \theta}{dt^2}=mgL \cos \theta$
  2. $I \dfrac{d^2 \theta}{dt^2}=mgL \sin \theta$
  3. $I \dfrac{d^2 \theta}{dt^2}=mgL \tan \theta$
  4. $I \dfrac{d^2 \theta}{dt^2}=mg \sin \theta$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Taking the torque about the point of suspension, we can write $I \dfrac{d^2 \theta}{dt^2}=mgL \sin \theta$

The correct option is (b)

Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

One end of spring of spring constant k is attached to the centre of a disc of mass m and radius R and the other end of the spring connected to a rigid wall. A string is wrapped on the disc and the end A of the string is pulled through a distance a and then released.
The disc is placed on a horizontal rough surface and there is no slipping at any contact point What is the amplitude of the oscillation of the centre of the disc?

  1. a

  2. 2a

  3. a/2

  4. none of these.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Displacement of the topmost point of the disc = a.
Disc undergoes rolling without slipping.
Hence the displacement of the centre of the disc = a/2
Thus the amplitude of the oscillation of the centre of the disc = a/2
Hence (C) is correct.

Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

The angular frequency of a torsional pendulum is $\omega$ rad/s. If the moment of inertia of the object is I, the torsional constant of the wire is related to the rotational kinetic energy of the disc, if the disc was rotating with an angular velocity $\omega$ is

  1. k= 2 KE

  2. k= KE

  3. k= 4 KE

  4. k= KE/2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

we know that $T=2 \pi \sqrt{I/k}$. Substituting the values given, we get, $k= I \omega^2 =2 \times $ kinetic energy

The correct option is (a)

Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

A small sphere is suspended by a string from the ceiling of a car. If the car begins to move with a constant acceleration $a$, the inclination of the string with the vertical is:-

  1. ${\tan ^{ - 1}}\left( {\dfrac{1}{2}} \right)$ in the direction of motion
  2. ${\tan ^{ - 1}}\left( {\dfrac{1}{2}} \right)$ opposite to the direction of motion
  3. ${\tan ^{ - 1}}\left( 2 \right)$ in the direction of motion
  4. ${\tan ^{ - 1}}\left( 2 \right)$ opposite to the direction of motion
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

A pendulum clock keeping correct time is taken to high altitudes,

  1. it will keep correct time

  2. its length should be increased to keep correct time

  3. its length should be decreased to keep correct time

  4. it cannot keep correct time even if the length is
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At high altitudes, g decreases. Since T = 2*pi*sqrt(l/g), T increases, meaning the clock runs slow. To keep correct time, T must be decreased, which requires decreasing the length l.

Multiple choice angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

Restoring force on the bob of a simple pendulum of mass $100\ gm$ when its amplitude is ${ 1 }^{ 0 } $ is 

  1. $0.017\ N$
  2. $1.7\ N$
  3. $0.17\ N$
  4. $0.034\ N$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The restoring force for a simple pendulum is F = mg*sin(theta). For theta = 1 degree, F = 0.1 * 9.8 * sin(1 degree) approx 0.1 * 9.8 * 0.01745 = 0.0171 N.