Tag: motion of system of particles and rigid bodies

Questions Related to motion of system of particles and rigid bodies

What is the position of centre of gravity of a cylinder?

physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

  1. At the center of base circle

  2. At the center of top circle

  3. Cannot be determined

  4. At the mid point on the axis of cylinder

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Correct Option: D
Explanation:

Centre of gravity means a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass. For regular shaped bodies it lies at the centre of the that particular body. Hence for a cylinder centre of gravity lies at the midpoint of the axis of the cylinder.

In an artificial satellite, the use of a pendulum watch is discarded, because :

physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

  1. The satellite is in a constant state of motion

  2. The effective value of $g$ becomes zero in the artificial satellite

  3. The periodic time of the pendulum watch is reduced

  4. None of these

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Correct Option: B

Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the periods of revolution of Mercury, Earth, Jupiter and Neptune and nearly 0.24, 1, 11.8 and 165 years. It follows that the period of revolution of
1. Venus is less than 0.24 years
2. Mars is less than 12 years
3. Uranus is more than 165 years
4. Uranus is less than 165 years but more than 12 years.

physics motion of system of particles and rigid bodies centre of gravity turning effects of forces forces - vectors and moments

  1. 1 and 3

  2. 4 only

  3. 3 o nly

  4. 2 and 4

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Correct Option: D

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.