Principles Of Rotational Mechanics And Static Equilibrium Practice Tests

Question 1

A force of $F = 25.0\, 	ext{N}$ is applied to a wrench at an angle of $60.0^\circ$ relative to the handle. If the force is applied at a distance of $0.400\, 	ext{m}$ from the pivot, calculate the magnitude of the moment in $	ext{N m}$.

Accepted Answer

8.66

Question 2

A uniform beam of length $L = 5.00\, 	ext{m}$ is pivoted at one end. A force of $50.0\, 	ext{N}$ is applied perpendicular to the beam at the far end. What is the moment of this force about the pivot?

Accepted Answer

250.0 N m

Answer

10.0 N m

Answer

50.0 N m

Answer

125.0 N m

Question 3

A see-saw is balanced with a $15.0\, 	ext{kg}$ mass placed $2.00\, 	ext{m}$ from the pivot. If a $10.0\, 	ext{kg}$ mass is placed on the opposite side to maintain equilibrium, calculate the distance in meters from the pivot where the $10.0\, 	ext{kg}$ mass must be placed. (Assume $g = 9.81\, 	ext{m/s}^2$)

Accepted Answer

3.00

Question 4

If the sum of clockwise moments about a pivot is $120\, 	ext{N m}$ and the sum of anticlockwise moments is $120\, 	ext{N m}$, the object is in rotational equilibrium.

Accepted Answer

True

Answer

False

Question 5

A $2.00\, 	ext{m}$ uniform rod weighing $100\, 	ext{N}$ is supported horizontally by a cable attached at the end at an angle of $30.0^\circ$ to the rod. What is the vertical component of the tension required to support the rod?

Accepted Answer

50.0 N

Answer

25.0 N

Answer

86.6 N

Answer

100.0 N

Question 6

Which of the following conditions must be satisfied for a rigid body to be in static equilibrium?

Answer

The sum of all forces acting on the body must be zero.

Answer

The sum of all moments about any pivot point must be zero.

Answer

The object must be moving at a constant velocity.

Answer

The net torque must be equal to the moment of inertia times angular acceleration.

Question 7

A $4.00\, 	ext{m}$ beam has a weight of $200\, 	ext{N}$ acting at its center. If the beam is supported at both ends, calculate the upward force in Newtons exerted by each support.

Accepted Answer

100

Question 8

A force $F$ is applied to a door at a distance $r$ from the hinge. If the angle between the force vector and the door is $	heta$, which expression correctly represents the moment?

Accepted Answer

$	au = F \cdot r \cdot \sin(	heta)$

Answer

$	au = F \cdot r \cdot \cos(	heta)$

Answer

$	au = F \cdot r \cdot 	an(	heta)$

Answer

$	au = \frac{F \cdot r}{\sin(	heta)}$

Question 9

An L-shaped lamina is formed by two uniform rectangular plates of mass $m_1 = 2	ext{ kg}$ and $m_2 = 4	ext{ kg}$. The centre of mass of the first plate is at $(1, 4)$ and the second at $(5, 2)$. Calculate the $x$-coordinate of the system's centre of gravity.

Accepted Answer

3.67

Question 10

A uniform rod of length $L$ is suspended from one end. If a mass $M$ is attached to the bottom end, how does the centre of gravity shift compared to the rod alone?

Accepted Answer

It shifts downward toward the attached mass.

Answer

It shifts upward toward the pivot.

Answer

It remains at the geometric center.

Answer

It moves outside the rod.

Question 11

A triangular lamina has vertices at $(0,0)$, $(6,0)$, and $(0,9)$. Determine the coordinates $(x, y)$ of its centre of gravity.

Accepted Answer

(2, 3)

Question 12

A bus with a track width $w = 2.5	ext{ m}$ and a centre of gravity height $h = 1.8	ext{ m}$ is on a ramp inclined at angle $	heta$. At what angle $	heta$ will the bus begin to topple?

Accepted Answer

$	heta = \arctan(\frac{w}{2h})$

Answer

$	heta = \arctan(\frac{w}{h})$

Answer

$	heta = \arcsin(\frac{w}{2h})$

Answer

$	heta = \arctan(\frac{2h}{w})$

Question 13

If the line of action of an object's weight falls exactly on the edge of its base, the object is in a state of impending toppling.

Accepted Answer

True

Answer

False

Question 14

A block of mass $m$ is placed on a slope. If the base width is $b$ and the height of the CG is $h$, which condition ensures the block remains stable?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 15

Which of the following actions increase the stability of a vehicle?

Answer

Lowering the centre of gravity

Answer

Increasing the height of the centre of gravity

Answer

Increasing the track width

Answer

Reducing the mass of the vehicle

Question 16

A sphere is placed on a flat horizontal surface. If it is slightly displaced, its centre of gravity remains at the same height. What type of equilibrium is this?

Accepted Answer

Neutral equilibrium

Answer

Stable equilibrium

Answer

Unstable equilibrium

Answer

Dynamic equilibrium

Question 17

A uniform beam of length $L = 4.00\, 	ext{m}$ and mass $M = 10.0\, 	ext{kg}$ is supported horizontally by a pivot at one end and a cable attached to the other end at an angle of $30.0^\circ$ to the horizontal. Calculate the tension $T$ in the cable required to maintain equilibrium.

Accepted Answer

98.0 N

Answer

49.1 N

Answer

196.2 N

Answer

392.4 N

Question 18

A block of width $w = 0.50\, 	ext{m}$ and height $h = 1.20\, 	ext{m}$ rests on a flat surface. Determine the maximum angle $	heta$ to which the surface can be tilted before the block begins to topple.

Accepted Answer

22.6°

Question 19

Which of the following modifications will increase the stability of an object resting on a horizontal surface?

Answer

Lowering the centre of gravity

Answer

Increasing the base area

Answer

Increasing the height of the centre of gravity

Answer

Reducing the mass of the object

Question 20

If a sphere is placed on a perfectly flat horizontal surface, it is in neutral equilibrium because any small displacement results in the centre of gravity remaining at the same height.

Accepted Answer

True

Answer

False

Principles Of Rotational Mechanics And Static Equilibrium Practice Tests

Practice Tests

Principles of Rotational Mechanics and Static Equilibrium

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