16 Marks Questions

Part - B

'16' Marks Questions

1. Define the centre of mass of a system of particles. Derive the expression for it.

2. Discuss centre of mass of continuous bodies.

3. Explain the motion of the centre of mass. 

4. Derive an expression for kinetic energy of system of particles.

5. Derive the equation of rotational motion about fixed axis.

6. Derive the relation between rotational kinetic energy and moment of inertia.

7. Derive an expression for the rotational kinetic energy of a rigid body rotating about a fixed axis with an angular velocity ω

8. State and prove the theorem of parallel axes for the moment of inertia of a rigid body.

9. State and prove the theorem of perpendicular axis for the moment of inertia of a plane lamina.

10. Derive an expression for the moment of inertia of a uniform rod.

(i) About an axis through its centre and perpendicular to its length.

(ii) About an axis passing through on end of the rod and perpendicular to its length.

11. Derive an expression for the moment of inertia of thin ring. 

(a) About an axis through its centre and perpendicular to its plane.

(b) about a diameter.

(c) about a tangent in the plane of the ring.

12. Derive an expression for the moment of inertia of a thin circular disc

(a) about an axis through its centre and perpendicular to its plane.

(b) about a diameter.

13. Derive an expression for the moment of inertia of a solid sphere.

(a) about diameter

(b) about a tangent

14. Derive an expression for the moment of inertia of a solid cylinder.

the centre and

(a) about an axis passing through perpendicular to its length a tematicamente

(b) about the axis of cylinder.

15. Discuss the moment of inertia of a diatomic molecule.

16. Derive an expression for angular momentum of a rigid body.

17. Explain conservation of angular momentum with examples. 

18. Discuss the rotational energy states of a rigid diatomic molecule.

19. Describe principle, construction and working of gyroscope. Mention its application in various fields.

20. Derive an expression for time period of torsion pendulum. Explain how it is used to find rigidity modulas of a wire.

21. Write notes on

(i) double pendulum

(ii) non-linear oscillations