A light cord is wrapped around the rim of the wheel disc of radius r and a steady downward pull F is exerted on the cord, then the angular acceleration of the wheel is

(1) $\frac{F}{Mr}$           (2) $\frac{2F}{M}$                 (3) $\frac{2F}{Mr}$                 (4) $\frac{M}{2F}$

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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected
(1) Moment of inertia

(2) Angular momentum

(3) Angular velocity

(4) Rotational kinetic energy

Concept Questions :-

Angular momentum
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A particle of mass 5 g is moving with a uniform speed of $3\sqrt{2}$cm/s in the x-y plane along the line y = $2\sqrt{5}$cm. The magnitude of its angular momentum about the origin in $\mathrm{g}-{\mathrm{cm}}^{2}/\mathrm{s}$ is

1.  0

2.  30

3.  $30\sqrt{2}$

4.  $30\sqrt{10}$

Concept Questions :-

Angular momentum
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Three-point masses, each of mass m are placed at the corners of an equilateral triangle of side a. The moment of inertia of this system ab5ut an axis along one Side of the triangle is

1.

2.  ${\mathrm{ma}}^{2}$

3.  ${\mathrm{ma}}^{2}\frac{3}{4}$

4.  $\frac{3}{2}{\mathrm{ma}}^{2}$

Concept Questions :-

Moment of inertia
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A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with an acceleration

1.  $\frac{\mathrm{g}}{3}$

2.  $\frac{\mathrm{g}}{2}$

3.  $\frac{2\mathrm{g}}{3}$

4.  g

Concept Questions :-

Torque
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A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the system

(1) increases

(2) decreases

(3) remains constant

(4) depends on sense of rotation

Concept Questions :-

Moment of inertia
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A disc is rotating With an angular speed of m. If a child sits on it, which of the following is conserved?

1.  kinetic energy

2.  potential energy

3.  linear momentum

4.  angular momentum

Concept Questions :-

Angular momentum
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The torque of a force -6$\stackrel{^}{i}$ acting at a point r = 4$\stackrel{^}{j}$ about origin will bee

(1) -24$\stackrel{^}{k}$

(2) 24$\stackrel{^}{k}$

(3) 24$\stackrel{^}{j}$

(4) 24$\stackrel{^}{i}$

Concept Questions :-

Torque
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A particle moves in a force field given by , where r is the unit vector along with the position vector $\stackrel{\to }{\mathrm{r}}$, then which is true?

1.  The torque acting on the particle is not zero

2.  The torque acting on the particle produces an angular acceleration in it

3.  The angular momentum of the particle is conserved

4.  The angular momentum of the particle increases.

Concept Questions :-

Angular momentum
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The ratio of rotational and translatory kinetic energies of the sphere is

1.  2/9

2.  2/7

3.  2/5

4.  7/2

Concept Questions :-

Rolling motion