**3 and 5 Marks Questions**

**It is very much essential to completely solve all the exercises (including the additional exercises) given in NCERT text book. **

- What are errors? Describe the propagation of errors in addition subtraction multiplication and division.
- What do you mean by the principle of homogenity of dimensions? Describe the applications of dimensional analysis.
- Derive the equations of uniformly accelerated motion (graphically)
- Define projectile motion. Derive expression for Time of Flight, Horizontal Range and maximum height of a projectile.
- Derive an expression for the trajectory of a projectile.
- Show that there are two possible angles of projection for obtaining the same range.
- Derive an expression for centripetal acceleration in Uniform Circular motion.
- Derive F=ma from Newton’s second law of motion.

- State and explain Newton’s laws of motion.
- Show that Newton’s I law and Third law can be derived from II law.
- A light inextensible string with ends connected to two unequal masses runs over a frictionless pulley and is free to move. Derive an expression for the acceleration of the masses and the tension in the string.
- State Impulse – momentum principle and explain its applications.
- Why does a cricket player pulls his hands backwards while taking a catch? Describe similar situations of the principle based on which he does so.
- Explain the cause of friction.
- Why friction is called a necessary evil?
- Describe the different methods used to reduce friction.
- Derive an expression for the maximum safe velocity of a car on a level road.
- What do you mean by banking of roads at curves? Derive and expression for the maximum safe velocity of a car on a banked road and hence derive the velocity at curve on a banked road for minimum wear and tear.
- Derive an expression for the minimum horizontal velocity to be given to a ball hanging vertically from a point so that it is able to just complete a vertical circular path.
- Derive expression for the tension in a string at the top and bottom position while a body attached to its end describes a vertical circle.
- State and prove work – Kinetic energy theorem
- State the principle of conservation of energy. Show that the total mechanical energy of a body falling freely from a height remains constant throughout its motion.
- Distinguish between elastic and inelastic collisions
- Show that there is always a loss of kinetic energy in ordinary inelastic collisions.
- Derive an expression for the velocities after elastic collision between two bodies.
- Discuss elastic collision in two dimensions
- Derive the relationship between momentum and kinetic energy.
- Two particles of different mass have the same momentum; which one has greater kinetic energy – the light body or the heavy body?
- Two particles of different mass have the same kinetic energy; which one has greater momentum – the light body or the heavy body?
- Define radius of gyration.
- Define moment of inertia.
- Derive an expression for the centre of mass of a two particle system.
- Derive an expression for the rotational kinetic energy of a rigid body
- Derive an expression for the angular momentum of a rigid body
- State the principle of conservation of angular momentum and explain its applications.

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