Tag: equilibrium of a rigid body

Questions Related to equilibrium of a rigid body

When a spinning top slows down, it begins to wobble. This phenomenon can be explained by

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. gyroscopic precession

  2. inertia of motion

  3. force of gravity

  4. more complicated types of motion are coming into play

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Correct Option: D
Explanation:

When the top slows down, air bouancy, gravitational force, inertial movement and other complicated motion concepts act on it resulting into wobbling of the top.

The COM of body in pure rotation does-

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. translation

  2. rotation

  3. remain steady

  4. none of these

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Correct Option: C
Explanation:

Net external force acting on a pure rotating body is zero i.e.  $F _{ext} = 0$

Thus acceleration of COM  $a _{cm} = \dfrac{F _{ext}}{M} = 0$
Hence the COM of body in pure rotation remain steady.

Find the new coordinates of the point (3, 4), if the origin is shifted to the point (1, 3).

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. (2, 1)

  2. (1, 2)

  3. (1, -2)

  4. (2, -1)

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Correct Option: A
Explanation:

Initially the origin was (0,0) and the point was (3,4). If the origin is now shifted to a new point (1,3), then the coordinates of the new point will be (X,Y)  with respect to the new origin(h=1, k=3).  Thus, (3,4) = (X+1, Y+3). Solving, we get, X=2 and Y=1

A bicycle tyre in motion has :

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. linear motion only

  2. rotatory motion only

  3. linear and rotatory motion

  4. vibratory motion only

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Correct Option: C
Explanation:

A bicycle tyre rotates around the center which causes forward motion of the bicycle. Therefore, both rotation and linear motion of tyre is involved. 

Which of the following statements can be suitable?

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Rotational motion is a type of circular motion.

  2. Circular motion is similar to rotational motion.

  3. Rotational and circular motion are fundamentally unrelated.

  4. None of these

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Correct Option: B
Explanation:

In circular motion, the body revolves around a certain axis. So that body posses a certain angular velocity, angular acceleration and frequency of rotation where these terms are used in rotational motion. Thus circular motion is said to be similar to rotational motion.

Which of the following cannot be considered an example of precession?

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. A spinning top

  2. A spinning wheel

  3. Rolling ball

  4. Spinning of the earth

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Correct Option: C
Explanation:

Spinning of top, spinning wheel and spinning of the earth are purely rotational motion whereas rolling ball exhibits both rotational motion as well as translational motion. As precession is described by rotational motion only, thus rolling of ball cannot be considered as an example of precession.

A solid sphere is given angular velocity $\omega _0 $ and then kept on rough horizontal surface gently. When sphere starts pure rolling its angular velocity $\omega$ is

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. $
    \dfrac{2}
    {5}\omega _0
    $

  2. $
    \dfrac{3}
    {5}$u

  3. $
    \dfrac{5}
    {7}
    $u

  4. $
    \dfrac{3}
    {7}\omega _0
    $

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Correct Option: C

A man stands at the centre of a turn table it extended horizontally, with a $5 kg$ mass hand. He is set into rotation with an angular of one revolution in $2s$. His new angular is he drops his hands to his sides is (Assume moment of inertia of the man is $6 \ kgm^2$. The distance of the wavelength from the axis is $1 m$and final distance is $0.2 m$)

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. $2.5 \ rev/s$

  2. $1.25 \ rev/s$

  3. $5 \ rev/s$

  4. None of these

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Correct Option: A

For a particle showing motion under the force $F=-5{ \left( x-2 \right)  }^{ 2 },$ the motion is

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Translatory

  2. Oscillatory

  3. SHM

  4. All of these

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Correct Option: B

For a particle showing motion under the force $F=-5{ \left( x-2 \right) },$ the motion is

physics rigid body dynamics motion of rigid body rigid body equilibrium of a rigid body

  1. Translatory

  2. Oscillatory

  3. SHM

  4. Both (2) & (3)

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Correct Option: D