# A constant torque acting on a uniform circular wheel changes its angular momentum from ${\mathrm{A}}_{0}$ to  in 4s. The magnitude of this torque is  1. $\frac{3{\mathrm{A}}_{0}}{4}$ 2.  3. ${\mathrm{A}}_{0}$ 4.

Subtopic:  Angular Momentum |
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Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D${}_{1}$ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s${}^{-1}$. Disc D${}_{2}$ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s${}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s${}^{-1}$) of the system is

1. 60

2. 100

3. 120

4. 40

Subtopic:  Angular Momentum |
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A body rolls down an inclined plane without slipping. The fraction of total energy associated with its rotation will be

Where k is radius of gyration of the body about an axis passing through centre of mass and R is the radius of the body.

Subtopic:  Rolling Motion (OLD NCERT) |
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In the following figure, a weight W is attached to a string wrapped round a solid cylinder of mass M mounted on a frictionless horizontal axle at O.

If the weight starts from rest and falls a distance h, then its speed at that instant is

1. Proportional to R

2. Proportional to $\frac{1}{R}$

3. Proportional to $\frac{1}{{R}^{2}}$

4. Independent of R

Subtopic:  Torque |
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A solid cylinder rolls down an inclined plane that has friction sufficient to prevent sliding. The ratio of rotational energy to total kinetic energy is

1.  $\frac{1}{2}$

2.  $\frac{1}{3}$

3.  $\frac{2}{3}$

4.  $\frac{3}{4}$

Subtopic:  Rolling Motion (OLD NCERT) |
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A swimmer while jumping into water from a height easily forms a loop in the air, if

1. He pulls his arms and legs in

2. He spreads his arms and legs

3. He keeps himself straight

4. None of the above

Subtopic:  Moment of Inertia |
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Assertion : A ladder is more apt to slip when you are high up on it than when you just begin to climb

Reason : At the high point on a ladder, the torque is large and on climbing up the torque is small

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false
Subtopic:  Torque |
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An inclined plane makes an angle of $30°$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

1.  $\frac{g}{3}$

2.  $\frac{5g}{7}$

3.  $\frac{2g}{3}$

4.  $\frac{5g}{14}$

Subtopic:  Rolling Motion (OLD NCERT) |
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The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances traveled by A and B in the same time interval, then

1.  x-2y

2.  x = y

3.  y=2x

4.   none of these

Subtopic:  Rolling Motion (OLD NCERT) |
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If a gymnast, sitting on a rotating stool, with his arms outstretched, suddenly lowers his hands

1.  the angular velocity increases

2.  his moment of inertia increases

3.  the angular velocity stays constant

4.  the angular momentum increases

Subtopic:  Angular Momentum |
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