Tag: motion of system of particles and rigid bodies

Quizzes (12) Questions (32)

Questions Related to motion of system of particles and rigid bodies

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

When the centre of gravity of a body lies at the point of suspension or support, the body is said to be in _____ equilibrium. Fill in the blank. 

  1. Stable equilibrium

  2. Unstable equilibrium

  3. Neutral equilibrium

  4. All of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium. Example: rolling ball.If the ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. This type of equilibrium is called neutral equilibrium.

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics
Which of the following is not a condition of equilibrium?

  1. <div>The resultant of all the forces acting on the body should be equal to zero.</div>

  2. <div>The resultant of all the forces acting on the body about the point of rotation should be equal to zero.</div>

  3. Both A and B

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

Both the above options are conditions for a body to be on equilibrium and for equilibrium, sum of anticlockwise moments about the axis of rotation must be equal to the sum of clockwise moments about the same axis.

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

Centre of gravity is lowered in _______ equilibrium. Fill in the blank. 

  1. Stable

  2. Unstable

  3. Neutral

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the center of gravity of a body lies below point of suspension or support, the body is said to be in stable equilibrium. For example a book lying on a table is in stable equilibrium.

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

An object is said to be in equilibrium when :
1. There is no resultant force acting on the object.
2. The total clockwise moments about any point is equal to the total anti-clockwise moments about the same point.
3. The object has no energy.

  1. 1 only

  2. 2 only

  3. 1 and 2 only

  4. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

An object is said to be in equilibrium when there is no resultant force acting on the object, the total clockwise moments about any point is equal to the total anticlockwise moments about the same point.

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

The bob of simple pendulum having length l, is displaced from mean position to an angular position with respect to vertical. If it is released, then velocity of bob at equilibrium position : 

  1. $\sqrt { 2g\ell (1-cos\theta ) }$

  2. $\sqrt { 2g\ell (1+cos\theta ) } $

  3. $\sqrt { 2g\ell cos\theta } $

  4. $\sqrt { 2g\ell } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Potential energy at extreme position = kinetic energy at mean position

$mg\ell (1-cos\theta )=\frac { 1 }{ 2 } m{ v }^{ 2 }$

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

If the potential energy of the molecule is given by $U = \dfrac {A}{r^{6}} - \dfrac {B}{r^{12}}$. Then at equilibrium position its potential energy is equal to

  1. $-A^{2}/ 4B$

  2. $A^{2}/ 4B$

  3. $2A/B$

  4. $A/2B$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At equilibrium, the force F = -dU/dr = 0. Differentiating U = A/r^6 - B/r^12 gives -6A/r^7 + 12B/r^13 = 0, so r^6 = 2B/A. Substituting this back into U gives A/(2B/A) - B/(2B/A)^2 = A^2/2B - B * A^2/4B^2 = A^2/2B - A^2/4B = A^2/4B.

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

A rope ladder with a length $\ell$ carrying a man ofmass $m$ at its end is attached to the basket ofballoon with a mass $\mathrm { M }$ . The entire system is in equilibrium in the air. As the man climbs up theladder into the balloon, the balloon descends bya height h. Then the potential energy of the man: 

  1. Increases by mg $( \ell - h )$

  2. Increases by mge

  3. Increases by mgh

  4. Increases by mg $( 2 \ell - h )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

A wheel rolling on a horizontal surface is an example of

  1. Stable equilibrium

  2. Unstable equilibrium&nbsp;

  3. Neutral equilibrium&nbsp;

  4. All of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Neutral equilibrium means that, with a small deviation, the body remains in equilibrium. An example is a wheel rolling on a horizontal surface. If you stop it at any point, the wheel will be in a state of equilibrium. A ball lying on a flat horizontal surface is in a state of neutral equilibrium.