The motor of an engine is rotating about its axis with an angular velocity of 100 rpm.  It comes to rest is 15 s, after being switched off.  Assuming constant angular deceleration.  What are the numbers of revolutions made by it before coming to rest?

(1) 12.5          (2) 40             (3) 32.6             (4) 15.6

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A T joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis passing through A and perpendicular to the plane of the joint,

1.  $\frac{2{\mathrm{mL}}^{2}}{3}$

2.  $\frac{{\mathrm{mL}}^{2}}{12}$

3.  $\frac{{\mathrm{mL}}^{2}}{6}$

4.  None of these

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Moment of inertia
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The moment of inertia of a loop of radius R and mass M, about any tangent line in its plane will be

(1) $\frac{3M{R}^{2}}{2}$

(2) $\frac{M{R}^{2}}{2}$

(3) $M{R}^{2}$

(4) $\frac{M{R}^{2}}{4}$

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Moment of inertia
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A hollow sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v = 0.5 m/ s. The kinetic energy of the sphere is

1.  0.1 J

2.  0.3 J

3.  0.5 J

4.  0.42 J

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Rolling motion
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A man of the mass M stands at one end of a plank of length L which lies at rest on a frictionless surfacé. The man walks to the other end of the plank. If the mass of the plank is $\frac{\mathrm{M}}{3}$, the distance that the man moves relative to the ground is

1.  $\frac{3\mathrm{L}}{4}$

2.  $\frac{\mathrm{L}}{4}$

3.  $\frac{4\mathrm{L}}{5}$

4.  $\frac{\mathrm{L}}{3}$

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Center of mass
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Ratio of total kinetic energy and rotational kinetic energy in the motion of a disc is

(1) 1:1

(2) 2:7

(3) 1:2

(4) 3:1

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Rolling motion
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A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of 3 kg mass is 16 m/s. The velocity of 6 kg mass is

(1) 4 m/s

(2) 8 m/s

(3) 16 m/s

(4) 32 m/s

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Linear momentum
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A cylinder is rolling over a surface. Which points on it move rectilinearly?

(1) All points on the curved surface of the cylinder.

(2) All points on the flat surfaces of the cylinder.

(3) All points on the axis of the cylinder.

(4) None of the above

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Rolling motion
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A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inerita of the rod about A is $\frac{{\mathrm{ml}}^{2}}{3}$ the initial angular acceleration of the rod will be

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Torque