Tag: rotational equilibrium

Questions Related to rotational equilibrium

Consider the following statements:
(a)  Change in momentum is impulse.
(b)  A body is momentarily at rest when it reverse the direction.
(c)  For stable equilibrium force has to be zero and potential energy should be minimum.
(d)  Force required to accelerate a mass in two perpendicular directions is never same.
Which of the above statements are correct?

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

  1. (b) and (c)

  2. (a) and (b)

  3. (a), (b) and (d)

  4. All of the above

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Correct Option: D
Explanation:

All of the above
Impulse = Force$\times$time = $m\Delta{v}$ = Momentum
A body will be at rest for a moment when it changes direction.
When a body is in equilibrium it always has minimum potential energy and no force is acting upon it.
Force is a vector quantity and hence its direction will result in different force quantity.

State whether given statement is True or False.

When any object is in equilibrium, the sum of all the forces acting on it is zero.

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

  1. True

  2. False

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Correct Option: A
Explanation:

When an object is not in equilibrium, net force acting on the body is not zero.
Therefore when some force acts on the object, it is in accelerated motion because, $F= ma$

Potential energy function $U(r)$ corresponding to the central force $F=K/r^{2}$ would be

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

  1. $-K/r$

  2. $-2K/r$

  3. $-r/K$

  4. $None of these$

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Correct Option: A
Explanation:
We know that as per definition of potential energy ( Only defined for conservative froces) ,
$U=\int -Fdr=-\dfrac{k}{r}$

When a body remains in the state of rest conditions under the influence of applied forces, the body is in 

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

  1. Dynamic equilibrium

  2. Static equilibrium

  3. Both

  4. None

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Correct Option: B
Explanation:

The equilibrium is of two types
(1) Static equilibrium
(2) Dynamic equilibrium
When a body remains in the state of rest under the influence of the applied forces, the body is in static equilibrium.

A body is in translatory equilibrium if:

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

  1. Resultant force on it is zero

  2. It is at rest

  3. It is in uniform motion

  4. All options are correct

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Correct Option: D
Explanation:

A body is said to be in translatory equilibrium when net external force acting on it is zero.

Also if no external force is acting on the body, then the body must be at rest or moving with constant velocity i.e moves in uniform motion. Hence option D is correct.

Forces are said to be in equilibrium, when their resultant is:

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

  1. $1$

  2. $0$ (Zero)

  3. Non zero

  4. All

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Correct Option: B
Explanation:

The forces which are acting at a point are called concurrent forces. These forces are said to be in equilibrium, when the resultant is zero.

Two forces acting at a point will be in equilibrium, when they are

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

  1. Equal

  2. Opposite

  3. Both

  4. None

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Correct Option: C
Explanation:

Two forces acting at a point will be in equilibrium.

Only when they are equal and opposite.

The resultant of all the forces acting on the body in static equilibrium should be equal to 

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

  1. One

  2. Zero

  3. Two

  4. More than one

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Correct Option: B
Explanation:

The resultant of all the forces acting the body should be equal to zero. The resultant moment of all the forces acting on the body about the point of rotation should be zero.

When a body remains in the same state of motion (translational or rotational) under the influence of the applied forces, the body is said to be

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

  1. Static equilibrium

  2. Dynamic equilibrium

  3. Both

  4. None

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Correct Option: B
Explanation:

When a body remains in the same state of motion (translational or rotational) under the influence of the applied forces, the body is said to be dynamic equilibrium.

A ball located at the bottom of a spherical deepening is in a state of _________ equilibrium. Fill in the blank. 

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

  1. Stable equilibrium

  2. Unstable equilibrium

  3. Neutral equilibrium

  4. All of the above

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Correct Option: A
Explanation:

Stable equilibrium means that, with small deviations of the body from this state, forces or moments of forces emerge which tend to return the body to the state of equilibrium. A ball located at the bottom of a spherical deepening is in a state of stable equilibrium.