Two blocks,
m1 = 1.0 kg and
m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its rotational inertia is 5.0 kgm
2, the acceleration of the system is
a.
(1/6)
g b.
(3/8)
g c.
(1/8)
g d.
(1/2)
g e.
(5/8)
g
[Ques. 2] In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kgm2/s) at the lowest point of its path relative to the center of the circle is approximately
![](data:image/png;base64,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)
a.
40
b.
10
c.
30
d.
20
e.
50
[Ques. 3] A uniform cylinder of radius
R, mass
M, and length
L rotates freely about a horizontal axis parallel and tangent to the cylinder, as shown below. The rotational inertia of the cylinder about this axis is
a.
![](data:image/png;base64,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)
.
b.
![](data:image/png;base64,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)
.
c.
MR2.
d.
![](data:image/png;base64,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)
.
e.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAArCAIAAABXWFfMAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAJNSURBVFhH7ZbbkYMwDEXpYEtICSkh/X+lhJSwJWQPXEUrbPGYYWL8wflghHRtXWTI7vDum8vfMS5/xyj9/S5g5ebM/OHjdrv9VNzv97Mszvy9Xq/UH3lTNOffHxN6PB5YGY/zw/P5PHF4UJ6vRRPcYq7l8MaRTNh9/X1E0HHcUf1VGATjoGMcypo/LWjjjy7+dsW+i/4otz9cD/zcFv21HF7Btj9qO4eHUth9hikmjUVzJHO2z5fani8DARuhXBHTTAI9sPT8pioJxSCI9SLqNvenjTb9ARp+I2mTitlHJggkkF6eiCH2IvavZNog80ctPsE6iN2BpT6oVPz5IVkMTDKuJCnhXgEZqovna9EW2j39M0Mb+Yt56WNGbnSN5y5N7m8/6icrRVcOoT561xOAZFxVikh/1B9b6+mjD+8KxVzJoBRMS2utlmH+JscbSBkhqQYE9JMmJov2scSVJbGaMvrTsumRFkGATGscMpS4ekCSlhLHpIiZuppydH7uT4OB+D6t+9MSlZY49P6xu8+VmN6xZayKIlMLanJ/rHEsNYe8ducLlYYr/mSurkKd8SWeqUn8aRkfl36N6sVk6CQNV81ASQ/SasxoH25jpibxxwOxZnS34A9IRjzpQaROKgN2n7UQpT+kPA2noLGvrGxD6Q9bPjliy57HzJ+GJ3/DMPRgMTlf0Csoi9xa7QyS70PIIoPs1B/IYr/+cNadv+iG+a38crZh5g8rGMIWAdf9/+V/j9IfBypk1ArnkZyvY6lTWfs+euDyd4y+/b3ffxTFhbrdCLKuAAAAAElFTkSuQmCC)
.
[Ques. 4] A uniform sphere of radius
R and mass
M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The rotational inertia of the sphere about this axis is
a.
![](data:image/png;base64,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)
.
b.
![](data:image/png;base64,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)
.
c.
![](data:image/png;base64,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)
.
d.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAArCAIAAABXWFfMAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAJNSURBVFhH7ZbbkYMwDEXpYEtICSkh/X+lhJSwJWQPXEUrbPGYYWL8wflghHRtXWTI7vDum8vfMS5/xyj9/S5g5ebM/OHjdrv9VNzv97Mszvy9Xq/UH3lTNOffHxN6PB5YGY/zw/P5PHF4UJ6vRRPcYq7l8MaRTNh9/X1E0HHcUf1VGATjoGMcypo/LWjjjy7+dsW+i/4otz9cD/zcFv21HF7Btj9qO4eHUth9hikmjUVzJHO2z5fani8DARuhXBHTTAI9sPT8pioJxSCI9SLqNvenjTb9ARp+I2mTitlHJggkkF6eiCH2IvavZNog80ctPsE6iN2BpT6oVPz5IVkMTDKuJCnhXgEZqovna9EW2j39M0Mb+Yt56WNGbnSN5y5N7m8/6icrRVcOoT561xOAZFxVikh/1B9b6+mjD+8KxVzJoBRMS2utlmH+JscbSBkhqQYE9JMmJov2scSVJbGaMvrTsumRFkGATGscMpS4ekCSlhLHpIiZuppydH7uT4OB+D6t+9MSlZY49P6xu8+VmN6xZayKIlMLanJ/rHEsNYe8ducLlYYr/mSurkKd8SWeqUn8aRkfl36N6sVk6CQNV81ASQ/SasxoH25jpibxxwOxZnS34A9IRjzpQaROKgN2n7UQpT+kPA2noLGvrGxD6Q9bPjliy57HzJ+GJ3/DMPRgMTlf0Csoi9xa7QyS70PIIoPs1B/IYr/+cNadv+iG+a38crZh5g8rGMIWAdf9/+V/j9IfBypk1ArnkZyvY6lTWfs+euDyd4y+/b3ffxTFhbrdCLKuAAAAAElFTkSuQmCC)
.
e.
![](data:image/png;base64,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)
.
[Ques. 5] The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.
![](data:image/png;base64,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)
a.
2.9 J
b.
2.6 J
c.
3.1 J
d.
3.4 J
e.
1.6 J
[Ques. 6] The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.
![](data:image/png;base64,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)
a.
18 J
b.
15 J
c.
12 J
d.
23 J
e.
26 J
[Ques. 7] If
M = 0.50 kg,
L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the rotational inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.
a.
3.7 kgm
2 b.
2.8 kgm
2 c.
3.2 kgm
2 d.
2.3 kgm
2 e.
3.9 kgm
2
[Ques. 8] A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s
2. What is the rotational inertia of the wheel?
a.
0.023 kgm
2 b.
0.027 kgm
2 c.
0.016 kgm
2 d.
0.019 kgm
2 e.
0.032 kgm
2
[Ques. 9] A mass (
M1 = 5.0 kg) is connected by a light cord to a mass (
M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of
M2 is 3.5 m/s
2. What is the rotational inertia of the pulley?
a.
0.29 kgm
2 b.
0.42 kgm
2 c.
0.20 kgm
2 d.
0.62 kgm
2 e.
0.60 kgm
2
[Ques. 10] An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux B through any area completely inside the solenoid, centered on the solenoid axis but at a 45 angle to the axis, so that it touches the inside of the solenoid, as shown below, is
![](data:image/png;base64,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)
a.
![](data:image/png;base64,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)
.
b.
![](data:image/png;base64,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)
.
c.
0a2nI.
d.
2
0a2nI.
e.
0.