A circular plate of diameter d is kept in contact with a square plate of an edge as shown in the figure. The density of the material and the thickness are the same everywhere. The center of mass of the composite system will be 1.  inside the circular plate

2.  inside the square plate

3.  at the point of contact

4.  outside the system

Concept Questions :-

Center of mass
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A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

1.  0.4 cm

2.  2.4 cm

3.  1.8 cm

4.  1.2 cm

Concept Questions :-

Center of mass
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From a circular disc of radius R, a square is cut out with a radius as its diagonal.  The centre of mass of remainder is at a distance (from the centre)

(1) $\frac{R}{\left(4\mathrm{\pi }-2\right)}$             (2) $\frac{R}{2\mathrm{\pi }}$                (3) $\frac{R}{\left(\mathrm{\pi }-2\right)}$                     (4) $\frac{R}{\left(2\mathrm{\pi }-2\right)}$

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A particle of mass m moves along line PC with velocity v as shown.  What is the angular momentum of the particle about P? (1) mvL                 (2) mvl                (3) mvr                  (4) zero

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Two bodies with moment of inertia  $\left({I}_{1}>{I}_{2}\right)$ and have equal angular momenta.  If KE of rotation are , then

(1) ${E}_{1}={E}_{2}$                (2) ${E}_{1}>{E}_{2}$                (3)  ${E}_{1}<{E}_{2}$              (4) ${E}_{1}\ge {E}_{2}$

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A mass m with velocity u strikes a wall normally and returns at the same speed. What is the magnitude of the change in momentum of the body when it returns

1.  4 mu

2.  mu

3.  2 mu

4.  0

Concept Questions :-

Linear momentum
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Three indentical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is Concept Questions :-

Center of mass
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Two particles of equal mass have coordinates (2m,4m,6m) and (6m,2m,8m). Of these one particle has velocity ${\mathrm{v}}_{1}=\left(2\stackrel{^}{\mathrm{i}}\right)$ m/s and another particle has velocity ${\mathrm{v}}_{2}=\left(2\stackrel{^}{j}\right)$ m/s at time t = 0. The coordinate of their centre of mass at time t = 1 s will be

1. (4m,4m,7m)

2. (5m,4m,7m)

3. (2m,4m,6m)

4. (4m,5m,4m)

Concept Questions :-

Center of mass
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The M.I. of a body about the given axis is 1.2 kg x ${\mathrm{m}}^{2}$ initially the body at rest. In order to the rotational kinetic energy of 1500 J, the angular acceleration of 25 rad/${\mathrm{sec}}^{2}$ must be about that axis for the duration of

1.  4 sec

2.  2 sec

3.  8 sec

4.  10 sec

Concept Questions :-

Rotation motion : Introduction
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A loop rolls down on the inclined plane. The fraction of its total kinetic energy that is associated with rotational motion is

1.  1: 2

2.  1: 3

3.  1: 4

4.  2: 3

Concept Questions :-

Rolling motion