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A

Group 'A'

Circle the best alternative to the following questions.

11 questions·1 marks each
1mcq1 marks

A metre rule is used to measure the length of a piece of string in a certain experiment. It is found to be 20 cm long to the nearest millimeter. How should this result be recorded in a table of results?

  • a

    0.2000m

  • b

    0.200m

  • c

    0.20m

  • d

    0.2m

measurementsignificant-figures
2mcq1 marks

Forces are applied to a rigid body. The forces all act in the same plane. In which diagram is the body in equilibrium?

Four force diagrams (a)-(d) on a circular rigid body

  • a

    Diagram (a): an upward F and a downward F offset (net torque non-zero).

  • b

    Diagram (b): two upward F and one downward 2F.

  • c

    Diagram (c): upward 2F and F, downward F and 2F balanced.

  • d

    Diagram (d): upward 2F and downward F, F.

staticsequilibrium-of-forces
3mcq1 marks

An athlete makes a long jump and follows a projectile motion. Air resistance is negligible. Which one of the following statements is true about the athlete?

Athlete at the top of a projectile (parabolic) path

  • a

    The athlete has constant horizontal and vertical velocities.

  • b

    The athlete has a constant horizontal velocity and constant downward acceleration.

  • c

    The athlete has a constant upward acceleration followed by a constant downward acceleration.

  • d

    The athlete has a constant upward velocity followed by a constant downward velocity.

projectile-motion
4mcq1 marks

At Kulekhani-I Hydro-power station, water flows from Indra Sarowar into the turbines that are a vertical distance of 550 m below the lake, as shown in the diagram. Generally, 780 000 kg of water flows into the turbines every minute. The turbines have the efficiency of 85%. What is the output power of the turbines?

Lake 550 m above a turbine

  • a

    71 MW

  • b

    60MW

  • c

    4.2 GW

  • d

    3.6 GW

work-energy-powerhydropower
5mcq1 marks

Graphs of stress-strain for four different materials are shown below. Which graph represents the stiffest material?

Four stress-strain graphs (a)-(d)

  • a

    Graph (a): steep straight line.

  • b

    Graph (b): curve levelling off.

  • c

    Graph (c): S-shaped curve.

  • d

    Graph (d): straight line (less steep).

elasticitystress-strainyoungs-modulus
6mcq1 marks

A boy walks towards a stationary plane mirror at a speed of 1.2ms11.2\,\text{ms}^{-1}. What is the relative speed of approach of the boy and his image?

  • a

    zero

  • b

    1.2 ms⁻¹

  • c

    2.4 ms⁻¹

  • d

    1.44 ms⁻¹

reflectionplane-mirror
7mcq1 marks

The critical angle between an equilateral prism and air is 4545^\circ. What happens to the incident ray perpendicular to the refracting surface?

  • a

    It is reflected totally from the second surface and emerges perpendicular from the third surface.

  • b

    It gets reflected from second and third surfaces and emerges from the first surface.

  • c

    It keeps reflecting from all the three sides of the prism and never emerges out.

  • d

    After deviation, it gets refracted from the second surface.

refractiontotal-internal-reflectionprism
8mcq1 marks

In the formation of a rainbow, the light from the sun on water droplets undergoes which of the following phenomenon/phenomena?

  • a

    dispersion only

  • b

    only total reflection.

  • c

    dispersion and total internal reflection

  • d

    scattering

dispersionrainbowtotal-internal-reflection
9mcq1 marks

In what unit is the power of a lens measured?

  • a

    watt

  • b

    metre

  • c

    dioptre

  • d

    Hertz

opticslensunits
10mcq1 marks

A piece of wire of resistance R is bent through 180180^\circ at mid-point and the two halves are twisted together. What is the resistance of the wire thus formed?

  • a

    R/4

  • b

    R/2

  • c

    R

  • d

    2R

current-electricityresistance
11mcq1 marks

What are the elementary particles with half spin called?

  • a

    quarks

  • b

    bosons

  • c

    fermions

  • d

    hadrons

modern-physicselementary-particles
B

Group 'B'

Answer the following questions.

8 questions·5 marks each
1short5 marks

(a) State the law of conservation of momentum. [2][2]

(b) A jumbo jet of mass 4×105kg4\times10^5\,\text{kg} travelling at a speed of 5000 m/s lands on the airport. It takes 2 minutes to come to rest. Calculate the average force applied by the ground on the aeroplane. [2][2]

(c) After landing the aeroplane's momentum becomes zero. Explain how the law of conservation holds here. [1][1]

OR

(a) State Hooke's law. [2][2]

(b) The walls of the tyres on a car are made of a rubber compound. The variation with stress of the strain of a specimen of this rubber compound is shown in Fig. 1.2. As the car moves, the walls of the tyres bend and straighten continuously. Use Fig. 1.2 to explain why the walls of the tyres become warm. [3][3]

Fig. 1.2 stress-strain hysteresis loop of rubber

momentumconservation-of-momentumelasticityhookes-law
2short5 marks

(a) What is meant by specific latent heat of vaporization of water =2.26MJ kg1=2.26\,\text{MJ kg}^{-1}? [1][1]

(b) A 1.0 kW kettle contains 500 g of boiling water. Calculate the time needed to evaporate all the water in the kettle. (Specific latent heat of vaporization of water =2.26MJ kg1=2.26\,\text{MJ kg}^{-1}). [3][3]

(c) Explain why the actual time needed is a little longer than the time calculated in (b). [1][1]

thermodynamicslatent-heat
3short5 marks

(a) State any three properties of an ideal gas as assumed by the kinetic theory of gas. [3][3]

(b) A student needed to use the ideal gas for a certain experiment. But, the ideal gas does not exist. Suggest what two different things this student could do to solve his problem. [2][2]

kinetic-theoryideal-gas
4short5 marks

(a) Define temperature gradient in an object. [1][1]

(b) An electric kitchen range has a total wall area of 1.40m21.40\,\text{m}^2 and is insulated with a layer of fibre glass at 175C175^\circ C inner and 35C35^\circ C outer surface. The fibre glass has thermal conductivity 0.040Wm1K10.040\,\text{Wm}^{-1}\text{K}^{-1}. Calculate the rate of flow of heat through the insulation (treat fibre as a flat slab of area 1.40m21.40\,\text{m}^2). [3][3]

(c) How might the rate of conduction be affected if the fibre absorbs moisture? Justify your answer. [1][1]

heat-transferconduction
5short5 marks

Figure 5.1 shows a ray of light entering and emerging through a part of a convex lens.

(i) Define 'convex lens', and state one daily application of it. [2][2]

(ii) Explain why this lens is also called converging lens. [1][1]

(iii) Calculate the refractive index of the material of the lens shown in the figure. [2][2]

Fig. 5.1 ray entering a convex lens with angles 54° and 32°

OR

(a) Define 'concave mirror' and state one daily application of it. [2][2]

(b) A certain projector uses a concave mirror that produces an image 5 times bigger than the object, with the screen 5 m away from the mirror (Fig. 5.2).

(i) Give reason why the image is larger than the object. [1][1]

(ii) Calculate the focal length of the mirror. [2][2]

Fig. 5.2 concave mirror projector, image and object, 5 m screen distance

geometrical-opticslensconcave-mirror
6short5 marks

(a) Sketch an electric field pattern around two identical negative point charges. [2][2]

(b) Obtain an equation, in terms of QQ and rr, for the field strength at point X due to two charges shown in Fig. 6.1. [3][3]

Fig. 6.1 two negative charges −Q each separated, point X to the right at distance r

electrostaticselectric-field
7short5 marks

(a) Define capacitance of a parallel plate capacitor and state one application of it in an electric circuit. [2][2]

(b) Three capacitors each of 1000μF1000\,\mu F are connected in an electric circuit as shown below (Fig. 7.1).

(i) Identify the type of combination shown in Fig. 7.1, and calculate the effective capacitance of the combination. [1+2][1+2]

Fig. 7.1 combination of three 1000 µF capacitors between X and Y

capacitancecapacitor-combination
8short5 marks

(a) What is meant by power of a heater is 2 kW? [1][1]

(b) Calculate the resistance of the above-mentioned heater when it is connected to 220 V source. [2][2]

(c) Suggest what changes must be done to the heater so that it gives more heat. Justify your answer. [2][2]

electric-powerresistanceheating-effect
C

Group 'C'

Give long answer to the following questions.

3 questions·8 marks each
9long8 marks

A box at rest is accelerated by a rope attached to a motor. The velocity-time graph below shows the pattern of its motion for 20 s.

Velocity-time graph rising linearly to 24 m/s at 10 s then constant

(a) If the box is pulled with constant unbalanced force 10 N, show that the initial acceleration of the box is 2.5ms22.5\,\text{ms}^{-2}, and calculate its mass. [2+1][2+1]

(b) After 2.0 seconds the box is being pulled by a constant force 12 N. Determine the size of frictional force acting on the box at this time. [2][2]

(c) Determine the distance the box travels along the ground at 8.0 s. [3][3]

dynamicsnewtons-lawskinematics-graph
10long8 marks

A boy is operating a remote-controlled toy car on a horizontal circular track of radius 1.8m1.8\,\text{m}; the car travels at constant speed.

Fig. 10.1 toy car on a horizontal circular track

(i) Explain why the car is accelerating, even though it is travelling at a constant speed. [2][2]

(ii) The car has mass 0.50kg0.50\,\text{kg}. The boy increases the speed to 6.0ms16.0\,\text{ms}^{-1}. The total radial friction between car and track has a maximum value of 7.0N7.0\,\text{N}. Show by calculation that the car cannot continue to travel in a circular path. [3][3]

(iii) The car is now placed on a track which includes a raised section (Fig. 10.2), an arc of a circle of radius r=0.85mr=0.85\,\text{m}. The car loses contact with the raised section if its speed exceeds vmaxv_{max}. Show that vmax=rgv_{max}=\sqrt{rg}. [3][3]

Fig. 10.2 raised section of track, arc radius 0.85 m, car on top

OR

Juno is a NASA orbiter in an elliptical orbit around Jupiter (see figure). The gravitational potential at point A in the orbit of Juno is 1.70×109J kg1-1.70\times10^9\,\text{J kg}^{-1}.

Juno orbiter in elliptical orbit around Jupiter, points A and B marked

(a) State what is meant by a gravitational potential at point A is 1.70×109J kg1-1.70\times10^9\,\text{J kg}^{-1}. [2][2]

(b) At point B, Juno is 1.69×108m1.69\times10^8\,\text{m} from the centre of Jupiter. If the mass of Jupiter is 1.90×1027kg1.90\times10^{27}\,\text{kg}, calculate the gravitational potential at point B. [3][3]

(c) The mass of Juno is 1.6×103kg1.6\times10^3\,\text{kg}. Determine the change in gravitational potential energy if Juno moves from Point A to Point B. [3][3]

circular-motiongravitation
11long8 marks

(a) Explain how Rutherford's α\alpha-scattering experiment suggested that the nucleus of an atom is very small, very dense and positively charged. [3][3]

(b) Considering that the α\alpha-particles carry average kinetic energy of 2.00×1010J2.00\times10^{-10}\,\text{J} (as printed), calculate the maximum size of the gold nucleus. [Atomic number of gold is 79 and e=1.60×1019Ce=1.60\times10^{-19}\,\text{C}] [3][3]

(c) Explain why the radius of the gold nucleus must be much smaller than the value calculated in (b) above. [2][2]

modern-physicsrutherford-scatteringnucleus