A wheel is rotating 900 rpm about its axis. When power is cut off it comes to rest in 1 min. The angular retardation in rad/s2 is

1. $\mathrm{\pi }/2$

2. $\mathrm{\pi }/4$

3. $\mathrm{\pi }/6$

4. $\mathrm{\pi }/8$

Concept Questions :-

Rotation motion : Introduction
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A particle of mass 2 kg located at the position  m has a velocity of 2 m/s. Its angular momentum about z-axis in kg-${\mathrm{m}}^{2}/\mathrm{s}$ is :

1. +4

2. +8

3. -4

4. -8

Concept Questions :-

Angular momentum
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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 is

1.

2.

3.

4.

Concept Questions :-

Torque
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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

Concept Questions :-

Torque
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In an orbital motion, the angular momentum vector is

1. Along the radius vector

2. Parallel to the linear momentum

3. In the orbital plane

4. Perpendicular to the orbital plane

Concept Questions :-

Angular momentum
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A particle of mass m moves with a constant velocity along 3 different paths DE, OA & BC. Which of the following statements is not correct about its angular momentum about point O?

(A) It is zero when it is at A and moving along OA.

(B) The same at all points along the line DE.

(C) Of the same magnitude but oppositely directed at B and  D.

(D) Increases as it moves along the line BC.

Concept Questions :-

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

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A body at rest breaks into two pieces of equal masses.  The parts will move

(1) in same direction

(2) along different lines

(3) in opposite directions with equal speeds

(4) in opposite directions with unequal speeds

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A bob of mass m attached to an inextensible string of length l is suspended from verticle support.  The bob rotates in a horizontal circle with an angular speed  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

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