For \(L = 3.0~\text{m,}\) the total torque about pivot A provided by the forces as shown in the figure is:

1. \(210 ~\text{Nm}\) 2. \(140 ~\text{Nm}\)
3. \(95 ~\text{Nm}\) 4. \(75 ~\text{Nm}\)

Subtopic:  Torque |
 59%
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For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?
1. A disc of radius \(a\)
2. a ring of radius \(a\)
3. a square lamina of side \(2a\)
4. four rods forming square of side \(2a\)

Subtopic:  Moment of Inertia |
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The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass is
1. \(\frac{L}{2 \sqrt{3}}\)
2. \(\frac{L^2}{12}\)
3. \(\frac{L}{\sqrt{3}}\)
4. \(\frac{L}{\sqrt{2}}\)

Subtopic:  Moment of Inertia |
 73%
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Two uniform, thin, identical rods, each of mass \(M\) and length \(l\) are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and are perpendicular to the plane of the cross?
1. \(\frac{Ml^2}{12}\)
2. \(\frac{Ml^2}{6}\)
3. \(\frac{Ml^2}{4}\)
4. \(\frac{Ml^2}{3}\)

Subtopic:  Moment of Inertia |
 77%
From NCERT
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If the linear momentum is increased by \(50\%\), the kinetic energy will increase by:
1. \(50\%\)
2. \(100\%\)
3. \(125\%\)
4. \(25\%\)

Subtopic:  Linear Momentum |
 64%
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A solid sphere, a hollow sphere, and a disc, all having the same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by  

1. the solid sphere
2. the hollow sphere
3. the disc
4. all will take the same time  
Subtopic:  Rolling Motion (OLD NCERT) |
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If the kinetic energy of a body increases by \(0.1\%,\) the percent increase of its momentum will be 
1. \(0.05\%\)
2. \(0.1\%\)
3. \(1.0\%\)
4. \(10\%\)

Subtopic:  Linear Momentum |
 71%
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A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

1.  Both together only when the angle of inclination of the plane is 450

2.  Both together

3.  Hollow cylinder

4.  Solid cylinder

Subtopic:  Rolling Motion (OLD NCERT) |
 62%
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One circular ring and one circular disc both having the same mass and radius. The ratio of their moments of inertia about the axes passing through their centres and perpendicular to planes will be

1. 1:1

2. 2:1

3. 1:2

4. 4:1

Subtopic:  Moment of Inertia |
 85%
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A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of topmost point relative to the bottommost point is

1. v

2. 2v

3. v/2

4. zero

 

Subtopic:  Rolling Motion (OLD NCERT) |
 71%
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