# A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> The tension in the string required to produce an angular acceleration of 2 revolutions s-2 will be: 1. 25 N 2. 50 N 3. 78.5 N 4. 157 N

Subtopic:  Rotational Motion: Dynamics |
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The ratio of the acceleration for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle 'θ' without slipping and slipping down the incline without rolling is:

1. 5:7

2. 2:3

3. 2:5

4. 7:5

Subtopic:  Rolling Motion |
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A small object of uniform density rolls up a curved surface with an initial velocity ‘ν’. It reaches up to a maximum height $\frac{3{\mathrm{v}}^{2}}{4\mathrm{g}}$ with respect to the initial position. The object is:
1. Solid sphere
2. Hollow sphere
3. Disc
4. Ring
Subtopic:  Rolling Motion |
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A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:

1. g/L
2. 2g/L
3. 2g/3L
4. 3g/2L

Subtopic:  Torque |
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When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

1. a line perpendicular to the plane of rotation

2. the line making an angle of 45o to the plane of rotation

4. the tangent to the orbit

Subtopic:  Angular Momentum |
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Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water, the center of mass of the system shifts by:

1. 3.0 m

2. 2.3 m

3. zero

4. 0.75 m

Subtopic:  Center of Mass |
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A solid cylinder of mass 3 kg is rolling on a horizontal surface with a velocity of 4 ms-1. It collides with a horizontal spring of force constant 200 Nm-1. The maximum compression produced in the spring will be:

1. 0.5 m

2. 0.6 m

3. 0.7 m

4. 0.2 m

Subtopic:  Rolling Motion |
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ABC is an equilateral triangle with O as its centre. F1, F2, and F3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero, then the magnitude of F3 is:

1. ${\mathrm{F}}_{1}+{\mathrm{F}}_{2}$

2. ${\mathrm{F}}_{1}-{\mathrm{F}}_{2}$

3. $\frac{{\mathrm{F}}_{1}+{\mathrm{F}}_{2}}{2}$

4. $2\left(\mathrm{F}+{\mathrm{F}}_{2}\right)$

Subtopic:  Torque |
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The instantaneous angular position of a point on a rotating wheel is given by the equation,
$\theta \left(t\right)$ = 2t3 – 6t2
The torque on the wheel becomes zero at:

1.  t= 0.5 s

2.  t= 0.25 s

3.  t= 2 s

4.  t= 1 s

Subtopic:  Rotational Motion: Kinematics |
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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:

1.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}/4$

2.  ${\mathrm{I}}_{0}+2{\mathrm{ML}}^{2}$

3.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}$

4.  ${\mathrm{I}}_{0}+{\mathrm{ML}}^{2}/2$

Subtopic:  Moment of Inertia |
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