Moment of interia of a squares of side fa about an axis through its centre of gr

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Question
Moment of interia of a squares of side fa about an axis through its centre of gravity, is
Options
A. b³/4
B. b⁴/12
C. b⁴/3
D. b⁴/8
E. b⁴/36.

Correct Answer

b⁴/12

Applied Mechanics problems

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1. A particle moving with a simple harmonic motion, attains its maximum velocity when it passes
Options
A. the extreme point of the oscillation
B. through the mean position
C. through a point at half amplitude
D. none of these.

5. If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and floor, is
Options
A. 0.25
B. 0.50
C. 0.67
D. 0.33
E. 0.75

6. The centre of gravity of a homogenous body is the point at which the whole
Options
A. volume of the body is assumed to be concentrated
B. area of the surface of the body is assumed to be concentrated
C. weight of the body is assumed to be concentrated
D. all the above.

7. From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. The c.g. of the remainder is at a height of
Options
A. 4.5 cm
B. 5.0 cm
C. 5.25 cm
D. 5.5 cm.

9. Pick up the correct statement from the following :
Options
A. If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities.
B. If a sphere impinges directly on an equal sphere which is at rest, then a fraction (1 - e²) the original kinetic energy is lost by the impact.
C. If a smooth sphere impinges on another sphere, which is at rest, the latter will move along the line of centres.
D. If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles.
E. All the above.

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