A wheel is rotating at the rate of 33 rev/min.  If it comes to stop in 20 s. Then, the angular retardation will be

(1) $\mathrm{\pi }\frac{\mathrm{rad}}{{\mathrm{s}}^{2}}$                          (2)

(3)               (4)

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A solid sphere is rotating about a diameter at an angular velocity $\omega$.  If it cools so that its radius reduces to $\frac{1}{n}$ of its  original value, its angular velocity becomes [MP PMT 2006]

(1) $\frac{\omega }{n}$                                (2) $\frac{\omega }{{n}^{2}}$

(3) $n\omega$                                (4) ${n}^{2}\omega$

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A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

1. Decreases continuously

2. Decreases initially and increases again

3. Remains unaltered

4. Increases continuously

Concept Questions :-

Angular momentum
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The total torque about pivot A provided by the forces shown in the figure, for L = 3.0 m, is :

1. 210 Nm

2. 140 Nm

3. 95 Nm

4. 75 Nm

Concept Questions :-

Torque
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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 2 a

4. four rods forming square of side 2 a.

Concept Questions :-

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. $\frac{L}{\sqrt{2}}$

Concept Questions :-

Moment of inertia
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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 inertial of the cross about an axis passing through the point at which the two rods are joined and perpendicular to the plane of the cross

1. $\frac{M{l}^{2}}{12}$

2. $\frac{M{l}^{2}}{6}$

3. $\frac{M{l}^{2}}{4}$

4. $\frac{M{l}^{2}}{3}$

Concept Questions :-

Moment of inertia
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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%

Concept Questions :-

Linear momentum
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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

Concept Questions :-

Rolling motion
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A bullet of mass m and velocity v is fired into a block of mass M and sticks to it. The final velocity of the system equals

1.

2.

3.

4.  None of these

Concept Questions :-

Linear momentum