Problems for Practice

Problems for Practice

1. A fly wheel of mass 500 kg. and diameter 2 metre makes 500 revolutions per minute. Assuming that whole of the mass is concentrated at the rim, find its angular velocity and moment of inertia.

[Ans. 52.4 rad / sec, 500 kg × m2]

2. Five masses each of 0.2 kg are placed on horizontal circular disc of negligible mass which can rotate about a vertical axis passing through its centre. If all the masses be equidistant from the axis and at a distance 5 cms from it; find the moment of inertia of the system.

[Ans. 25 × 10-4 kg × m2] 

3. A ring of mass 5 kg, and radius 20 cms. rolls along the ground at the rate of 10 metres per second. Calculate its kinetic energy.

[Ans. 500 joule]

4. Calculate the kinetic energy of uniform circular disc of mass 1 kg and diameter 0.1 m, making 100 revolutions per minute about its axis.

[Ans. 6.7875 x 10-2 joules] 

5. A solid spherical ball rolls on a table. Determine the faction of its total kinetic energy that is rotational.

[Ans. 2/7]

6. A solid sphere of mass 0.1 kg and diameter 0.025 m rolls without slipping with a velocity 0.1 m/sec. Calculate its total kinetic energy in joules.

[Ans. 7 × 10-4 joules] 

7. Deduce the moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the bond length. Given internuclear distance = 1.3 Å.

[Ans. 2.79 × 10-47 kgm 2] 

8. Calculate the moment of inertia of a uniform disc of mass 0.2 kg and radius 5 cm about an axis passing through its edge and perpendicular to the plane of the disc.

[Ans. 7.5 × 10-4 kg · m2]