__IMPORTANT LONG QUESTIONS__
Q. 1 (a) Define rectangular components of a vector. Describe the method of addition of vectors by rectangular components.

(b) Explain scalar/dot product of two vectors. Write down its any four characteristics.

Q. 2 (a) Explain vector/cross product of two vectors. Write down its any four characteristics.

(b) Define torque. Calculate the torque due to force acting on a rigid body.

Q. 3 (a) Define isolated system. State and explain the law of conservation of linear momentum.

(b) Define elastic and inelastic collision. Explain elastic collision in one dimension to show that the relative velocities before and after collision are same.

Q. 4 (a) Discuss the elastic collision of two smooth balls in one dimension and find their velocities after the collision.

(b) Define projectile motion. Derive mathematical formula for its maximum height, time of flight, range and maximum range.

Q. 5 (a) Define gravitational field. Show that gravitational field is conservative OR the work done in gravitational field is independent of the path followed.

(b) Define energy. State and prove work-energy principle.

Q. 6 (a) Define absolute potential energy. Derive its mathematical expression.

(b) Explain inter-conversion of potential energy and kinetic energy.

Q. 7 (a) Define escape velocity and derive its formula. Also calculate its value on the surface of Earth.

(b) What is centripetal force? Derive relations for centripetal force and centripetal acceleration.

Q. 8 (a) What is rotational kinetic energy? Find the rotational kinetic energy of the disc and hoop.

(b) What are geo-stationary satellites? Derive the relation for radius of geo-stationary orbit.

Q. 9 (a) Define terminal velocity. Show that terminal velocity of a fog droplet is directly proportional to the square of its radius.

(b) State and explain equation of continuity.

Q. 10 (a) State and explain Bernoulli's equation.

(b) State and explain Torricelli's theorem.

Q. 11 (a) Define simple harmonic motion. Show that the motion of projection of a body moving along a circular path is SHM.

(b) Derive the expressions for instantaneous displacement, instantaneous velocity and instantaneous acceleration of a particle moving in a circle of radius xo.

Q. 12 (a) What is simple pendulum? Show that the motion of simple pendulum is SHM. Also find relations for its time period and frequency.

(b) Prove that energy is conserved for a body executing simple harmonic motion.

Q. 13 (a) What was Newton's formula for the speed of sound? What was drawback in it, how was it corrected by Laplace?

(b) What is interference of sound waves? Describe its types and conditions.

Q. 14 (a) Show that frequencies of stationary waves in a stretched string are quantized. (fn = nf1)

(b) What is Doppler effect? Describe its different cases.

Q. 15 (a) Describe Young's double slit experiment for demonstration of interference of light. Derive an expression for fringe spacing.

(b) Describe the principle, construction and working of Michelson's interferometer.

Q. 16 (a) Describe the diffraction of X-rays through crystals. Also derive Bragg's equation.

(b) What is compound microscope? Describe its construction and working. Also calculate its magnifying power.

**Q. 17. Solve the following numerical problems.**

**Q. 18. Solve the following numerical problems.**

**Q. 19. Solve the following numerical problems.**

**Q. 20. Solve the following numerical problems.**