14. Derive a relation between rotational Kinetic Energy of a
rigid body and its moment of inertia?
15. Calculate the work done in splitting a drop of water of
radius 1 cm to 106
droplets. Given surface Tension of water =
17. State Camot's theorem. Calculate lhe efficiency of a
Carnat's engine working between temperatures O0C and 100°C.
18. Show that the vertical oscillations of a loaded spring are simple
19. Derive the equations of motion.
2. s = ut + 1/2 at2
by graphical method.
20. Derive an expression for the horizontal range of
a projectile and calculate the angle at Projection for obtaining maximum
21. Calculate the
acceleration of the body and tension in the string in the following diagram.
Given g = 10 mls2.
Assume that there is no friction.
Derive an expression for F in the following diagram to give an acceleration a to
the body of mass m if the co-efficient of friction between the body and the
plane is µ and the angle made by the inclined plane with the horizontal is θ
23. Derive an expression for the
velocities after a perfectly elastic collision between two bodies of masses m,
and rn, moving with velocities u1 and u2 in the same direction.
24. A dumb - bell formed by two masses 2 be
kg each separated by a massless rod 20 cm long is rotating with angular velocity
10 rad/s about an axis passing through the mid point of the rod and perpendicular to its length. What
the new angular velocity if
each mass is suddenly displaced by 5 cm towards the centre.
The moment of inertia of a ring of mass 1 kg is 10-4 kg m2
about an axis passing through its centre and perpendicular to its plane. Calculate its
radius. What will be its moment of inertia about an axis.
a. along its diameter.
b. Along its tangent
25. Describe the variation of acceleration due to gravity (g)
with depth and draw a graph showing the variation of g as one moves outwards from the
centre of earth. (gv5 r graph)
Assuming that the VISCOUS force F of a spherical body moving through a
liquid depends on
1. the co·efficient of viscosity
2. the radius (r) of the spherical body.
3. the speed (v) of the body, derive an expression for F (stokes
law) by the method of dimensions.
27. Describe the principle of Carnot's refrigerator with diagram
and derive expression for its co-efficient of performance.
28. What is Doppler effect? Derive expression for the apparent
frequency sensed by a stationary listener when the source is (a) approaching and (b)
a. What are damped oscillations ? Draw graph showing the
variation of displacement with time for damped harmonic oscillations.
b. Derive expression for displacement, velocity and acceleration
in SHM using circle of reference concept.
29. a. State any four postulates of kinetic theory of gases.
b. Derive an expression for pressure exerted by ail ideal gas in
a container using kinetic theory of gases.
a. Derive Boyle's Law and Charles law using kinetic theory of
b. Explain the kinetic interpretation of temperature and hence
define absolute zero?
c. Calculate the average kinetic energy of a molecule of an ideal gas at 400