Rewrite the correct option in your answer sheet. [1 × 11 = 11]

1. The dimensional formula of the bulk modulus for a material is

(a) [ ML^{2}T^{-2 }]

(b) [ ML^{-1}T^{-2} ]

(c) [ MLT^{-2} ]

(d) [ ML^{2}T^{-3} ]

2. If the magnitude of the resultant of two vectors is equal to the magnitude of either of the two vectors, the two vectors should be inclined to each other by an angle of

(a) 120°

(b) 130°

(c) 60°

(d) 100°

3. The kinetic energy of an object in terms of its mass m and momentum p is

(a) K = 1/2 mv^{2}

(b) K = p^{2}/m

(c) K = p^{2}/2m

(d) K = 2p/m^{2}

4. An object is said to be in equilibrium if

(a) it is moving with a uniform velocity

(b) no net torque is applied on it

(c) no unbalanced force acts on it

(d) any above condition is satisfied

5. A solid ball of metal tied at the end of a string is revolved in a vertical circle. The tension in the string will be the greatest

(a) at the highest point of the circle

(b) at the lowest point

(c) at the two points when the string is horizontal

(d) at all points in the course of revolution

6. Which of the following statements about an image is incorrect?

(a) A virtual image is always upright

(b) A virtual image is either diminished or magnified

(c) A real image is always diminished

(d) A real image is always inverted

7. If the critical angle for a medium is 48.8°, the refractive index of the material medium is

(a) 1.50

(b) 1.33

(c) 1.65

(d) 2.42

8. A plano-convex lens has a focal length of 20 cm and its refractive index is 1.5. So the radius of curvature of this lens is

(a) 10 cm

(b) 40 cm

(c) -10 cm

(d) 15 cm

9. Chromatic aberration can be corrected by using an achromatic doublet which means

(a) a combination of converging and diverging lenses

(b) a combination of a convex lens and a concave lens

(c) a combination of a convex lens and a concave lens of different materials

(d) a combination of converging and diverging lenses of the same material

10. If the electric field intensity close to a charged object is uniform, the electric lines of force are drawn to be

(a) circular

(b) parallel

(c) converging

(d) diverging

11. In a semiconductor, the conduction of current is due

(a) only to holes

(b) only to electrons

(c) to holes and electrons

(d) only to ions

**Group "B"**

Answer the following short questions. [5 × 8 = 40]

1. (a) What do you mean by a free-body diagram? [1]

(b) A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle 37.0˚ below the horizontal and the chair slides along the floor. Draw a clearly free-body diagram for the chair. Use your diagram and Newton's laws to calculate the normal force that floor exerts on the chair. [3]

(c) When a bullet is fired from a gun, the total momentum before firing is zero. Is the total momentum of the bullet and gun zero after firing as well? How does this principle hold in this case? [1]

**OR**

(a) State Hooke’s law in terms of stress and strain. What is the constant of proportionality called in general? [1]

(b) Explain any two portions such as OA and AB of the stress-strain curve as shown in the given figure 1. Which portion does give information about the breaking stress? [3]

(c) What is the cause of elasticity of an object? [1]

2. (a) What do you mean by bimetallic strip? [1]

(b) Wooden scale can give more correct readings than metal scale. Justify your answer. [1]

(c) A copper cylinder is initially at 20.0°C. At what temperature will its volume be 0.150% larger than when it is at 20.0°C?

(The coefficient of cubical expansivity for copper = 5.10 × 10^{-5 }°C^{-1}.) [3]

3. (a) Why are gas laws not obeyed at low temperature and high pressure? Explain this in regard to the postulates of kinetic theory of gasses. [2]

(b) According to the kinetic theory of gases, the pressure exerted by the gas on a container is given by where the symbols carry their usual meanings. Using the pressure formula, obtain the equation of state for the ideal gas. [2]

(c) What is the physical meaning of molar gas constant, R? [1]

4. (a) What is a perfect black body? [1]

(b) A sphere of 4 cm diameter behaves like a black body. At what rate is energy radiated by the sphere if it is maintained at 600°C? (The Stefan’s constant = 5.67 × 10^{-8} W m^{–2} K ^{–4} ). [3

(c) During the winter, an animal curls into a ball. Does the body surface of the animal matter while losing energy? [1]

5. (a) Define the angle of deviation. Why does a ray of light passing through a prism deviate? Explain it with the aid of a ray-diagram. [2]

(b) A ray of light incident at an angle of 49° on a solid transparent equilateral prism suffers a minimum deviation. Show that the material of the prism is glass. [3]

**OR**

(a) An extended object AB is placed within the principal focus of a convex lens as shown in figure 2. Complete the ray diagram to locate the position of the image formed. [1]

(b) An object 6 cm high is placed at a distance of 30 cm from a concave lens of focal length 15 cm. Find the position and the size of the image. Is the image real or virtual? [3]

(c) A ray of light passing through the optical center of the lens will not deviate. Why? [1]

6. (a) What is an equipotential surface? [1]

(b) There are two unlike point charges separated by a fixed distance. Is there an equipotential surface between such charges? [1]

(c) Two large parallel metal plates carry opposite charges. They are separated by 10 cm and a potential difference of 500 V is applied between the plates. What is the magnitude of the electric field strength between the plates? Compute the work done by this field on a charge of 2.0 nC as it moves from the higher to the lower potential. [3]

7. (a) What do you mean by a parallel plate capacitor? [1]

(b) Show that by insertion of a dielectric between the plates of the capacitor, its capacitance increases. [2]

(c) Suppose the earth is an isolated spherical capacitor. If so, then calculate the capacitance of the earth of radius 6400 km.

8. (a) On what factors does the resistance of a metal wire depend? Define the resistivity of the material of the wire. [2]

(b) Compute the equivalent resistance of the network in figure 3 and find the current in each resistor. Also calculate the total power dissipation in the equivalent resistance. The battery has negligible internal resistance. [3]

**Group 'C' **

9. (a) A package falls out of an airplane that is flying in a straight line at a constant altitude and speed. If you could ignore air resistance, what would be the path of the package as observed by the pilot? As observed by a person on the ground? [2]

(b) Define the maximum height and time of flight of a projectile. [2]

(c) A projectile is fired with a velocity of 32 m/s at an angle of 30˚ to the horizontal. Find (i) the time to reach its greatest height, (ii) its horizontal range. With the same velocity what is the maximum possible range? (g = 10 m/s^{2} ). [3]

(d) What about the trajectory of the package if air resistance is considered into account?

10. (i) Distinguish between elastic and inelastic collisions. [2]

(ii) A 4 kg ball moving with a velocity of 10.0 m/s collides with a 16 kg ball moving with a velocity of 4.0 m/s in the opposite direction. Show that the total kinetic energy of two colliding balls is not conserved during the collision. Where does all that lost energy go? [3]

(iii)A 3 kg block moving to the right at 5 m/s makes a perfectly elastic collision with a 1.5 kg block moving to the right at 4 m/s. Find their velocities after collision.

**OR**

(i) Why is a force necessary to keep a body moving with a uniform speed in a circular motion? What is the necessary force that keeps the artificial satellites to move around the earth in circular motion? [3]

(ii) What are geostationary satellites? What are their uses? [2]

(iii)Obtain the value of g from the motion of the moon, assuming that its period of rotation round the earth is 27 days and 8 hours and that the radius of its orbit is 60.1 times the radius of the earth. (Radius of the earth = 6.36 × 10^{6} m).11. (a) Explain the quark combination of a proton and a neutron. [2]

(b) Point out the differences between nuclear fission and nuclear fusion. [3]

(c) The mass of

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