# A body of mass M and radius R is rolling horizontally without slipping with speed v.  It then rolls up a hill to a maximum height h.  If $h=\frac{5{v}^{2}}{6g}$, what is the M.I of the body? 1. $\frac{M{R}^{2}}{2}$                   2.  3.                 4.

Subtopic:  Rolling Motion |
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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 |
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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 |
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The figure shows a uniform solid block of mass M and edge lengths a, b and c. Its M.O.I. about an axis through one edge and perpendicular (as shown) to the large face of the block is

1. $\frac{M}{3}\left({a}^{2}+{b}^{2}\right)$

2. $\frac{M}{4}\left({a}^{2}+{b}^{2}\right)$

3. $\frac{7M}{12}\left({a}^{2}+{b}^{2}\right)$

4. $\frac{M}{12}\left({a}^{2}+{b}^{2}\right)$

Subtopic:  Moment of Inertia |
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The moment of inertia of a cube of mass m and side a about one of its edges is equal to

1.

2.

3.

4.

Subtopic:  Moment of Inertia |
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If the net external forces acting on the system of particles is zero, then which of the following may vary ?

1. Momentum of the system

2. Velocity of centre of mass

3. Position of centre of mass

4. None of the above

Subtopic:  Center of Mass |
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A constant torque of 1000 N-m turns a wheel of moment of inertial 200 $\mathrm{kg}-{\mathrm{m}}^{2}$ about an axis through its centre. Its angular velocity after 3 s is

Subtopic:  Torque |
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Point masses ${\mathrm{m}}_{1}$ and ${\mathrm{m}}_{2}$ are placed at the opposite ends of a rigid of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\mathrm{\omega }}_{0}$ is minimum is given by

Subtopic:  Rotational Motion: Dynamics |
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A circular disc of radius r has a uniform thickness.  A circular hole of diameter equal to the radius of the disc has been cut out as shown.  The centre of gravity of the remaining disc lies on the diameter of the disc at a distance x to the left of the centre of the original disc.  The value of x is

1. r

2. $\frac{r}{2}$

3. $\frac{r}{4}$

4. $\frac{r}{6}$

Subtopic:  Center of Mass |
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A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force '$\stackrel{\to }{\mathrm{F}}$' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

1.  $\frac{4}{3}l$

2.  I

3.  $\frac{2}{3}l$

4.  $\frac{3}{2}l$

Subtopic:  Center of Mass |
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