# A cylinder of mass 'M' is suspended by two strings wrapped around it as shown. The acceleration 'a' and the tension T when the cylinder falls and the string unwinds itself are, respectively,               1.   2.   3.   4.

Subtopic:  Rolling Motion (OLD NCERT) |
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An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

1. 350 N-m

2. 440 N-m

3. 531 N-m

4. 628 N-m

Subtopic:  Torque |
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PMT - 2000
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In an orbital motion, the angular momentum vector is

2. Parallel to the linear momentum

3. In the orbital plane

4. Perpendicular to the orbital plane

Subtopic:  Angular Momentum |
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AIIMS - 2004
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A particle of mass m moves with a constant velocity along 3 different paths, DE, OA and BC. Which of the following statements is not correct about its angular momentum about point O?

 1 It is zero when it is at A and moving along OA. 2 The same at all points along the line DE. 3 Of the same magnitude but oppositely directed at B and  D. 4 Increases as it moves along the line BC.

Subtopic:  Angular Momentum |
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Subtopic:  Angular Momentum |
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A sphere is rolling down a plane of inclination $\theta$ to the horizontal.  The acceleration of its centre down the plane is

1. g sin $\theta$

2. less than g sin $\theta$

3. greater than g sin $\theta$

4. zero

Subtopic:  Rolling Motion (OLD NCERT) |
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A bob of mass m attached to an inextensible string of length l is suspended from vertical support.  The bob rotates in a horizontal circle with an angular speed $\mathrm{\omega }$ $\mathrm{rad}/\mathrm{s}$ about the vertical.  About the point of suspension.

 1 Angular momentum is conserved 2 Angular momentum changes in magnitude but not in the direction 3 Angular momentum changes in direction but not in magnitude 4 Angular momentum changes both in direction and magnitude

Subtopic:  Angular Momentum |
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In free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet - block system is at a distance of

1. $\frac{\left(D-d\right)}{M+m}$ from the bullet

2. $\frac{md+MD}{M+m}$ from the block

3. $\frac{2md+MD}{M+m}$ from the block

4. $\frac{\left(D-d\right)M}{M+m}$ from the bullet

Subtopic:  Center of Mass |
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Blocks A and B are resting on a smooth horizontal surface given equal speeds of 2 m/s in the opposite sense as shown in the figure.

At t = 0, the position of blocks are shown, then the coordinates of centre of mass at t = 3s will be

1.  (1, 0)

2.  (3, 0)

3.  (5, 0)

4.  (2.25, 0)

Subtopic:  Center of Mass |
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A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is