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

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

  1. Translatory

  2. Oscillatory

  3. SHM

  4. Both (2) & (3)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The force F = -5(x-2) is a linear restoring force of the form F = -k(x-x0). This is the definition of Simple Harmonic Motion (SHM). Since all SHM is also oscillatory, both options (2) and (3) are correct.

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

Ram says, $'A$ body may be in pure rotation in the presence of a single external force, 'Shyam says, 'This is possible only for a rigid body', then:

  1. Ram's statement is correct

  2. both statements are correct in different situations

  3. both statements are wrong

  4. both statements are stated by physicists
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A single external force acting on a body will cause both translational and rotational acceleration if the line of action does not pass through the center of mass. A body can be in pure rotation only if the net force is zero or if the body is constrained (like a hinge), so Ram's statement is incorrect. Shyam's statement is also incorrect because pure rotation is not exclusive to rigid bodies, and a rigid body can still undergo translation under a single force.

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

What torque will increase angular velocity of a solid disc of mass $16kg$ and diameter $1m$ from zero to $2$rpm in $8s$?

  1. $\cfrac { \pi }{ 4 } N-m$

  2. $\cfrac { \pi }{ 2 } N-m$

  3. $\cfrac { \pi }{ 3 } N-m$

  4. $\pi N-m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Torque $\left( \tau  \right) =I\alpha $
$\tau =\cfrac { 1 }{ 2 } \times M{ R }^{ 2 }\times \cfrac { 2\pi \left( { n } _{ 2 }-{ n } _{ 1 } \right)  }{ t } $
$\therefore$ $\tau =16\times { \left( \cfrac { 1 }{ 2 }  \right)  }^{ 2 }\times \pi \cfrac { \left( 2-0 \right)  }{ 8 } =\pi N-m$

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

Any point on the circumference of a rigid body which is rolling without slipping undergoes :

  1. a circular path

  2. an elleptic path

  3. a cycloid path

  4. an parabolic path
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Any point on the rigid body, undergoing rolling without slipping, will have linear and angular speed, such that

$linear\ speed = distance\ from\ CoM \times angular\ speed$

Such particles follows cycloid path.

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

Rolling without slipping is an example of

  1. Rotation

  2. Translation

  3. Rotation with translation

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

When a body is rolling without slipping on the ground, its center of mass exhibits translational motion whereas the body exhibits rotational motion in its center of mass frame. Thus rolling body exhibits both translational motion as well as rotational motion.

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

A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water, the tension in the string is $T _0$. Find the difference between tension when the ship is sailing with a velocity $v$.

  1. $m v\omega$

  2. $2 mv \omega$

  3. $\displaystyle \frac{mv \omega}{2}$

  4. $\sqrt{2} m v \omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 Additional force is Coriolis force which acts perpendicular to the plane of motion. so $\Delta T=2mv\omega $ . 

 This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere.

Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

Choose the correct answer from the alternatives given.
An electromagnetic wave of frequency $\nu= 3\ MHz$ passes from vacuum  into a dielectric medium with permittivity $\varepsilon= 4$. Then

  1. wavelength and frequency both become half.

  2. wavelength is doubled and frequency remains unchanged.

  3. wavelength and frequency both remain unchanged.

  4. wavelength is halved and frequency remains unchanged.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given : frequency $v =3 MHz=3\times10^6Hz$, relative permitivity $\varepsilon _r = 4$
Here the frequency of electromagnetic wave remains unchanged but the wavelength of electromagnetic wave changes when it passes from one medium to another.
The refractive index is the square root of permeability and permittivity product. 
For formula,
$c=\dfrac 1{\sqrt {\mu _0\varepsilon _0}}\\\implies c\propto \dfrac1{\sqrt{\varepsilon _0}}$
Similarly,
$v\propto\dfrac1{\sqrt{\varepsilon}}$
Therefore,
$\dfrac cv=\sqrt{\dfrac {\varepsilon}{\varepsilon _0}}=\sqrt{\dfrac 41}=2........(i)$
But
$\dfrac cv=\dfrac {\nu\lambda}{\nu\lambda'}\\\implies \dfrac cv=\dfrac{\lambda}{\lambda'}\\\implies 2=\dfrac{\lambda}{\lambda'}\\\implies \lambda'=\dfrac \lambda2$
Hence wavelength is halved.