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CLASS 9 MATHEMATICS

  1. Mathematics Chapter 1 & 2

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CLASS 9 SCIENCE

  1. Class 9 Lesson 1, 6 & 8

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CLASS 10 MATHEMATICS

  1. CBSE Class 10 Mathematics Sample Paper 2018-19

    CBSE Class 10 Mathematics Marking Scheme 2018-19

  2. CBSE Class 10 Mathematics Sample Paper 2017-18

    CBSE Class 10 Mathematics Marking Scheme 2017-18

  3. CBSE Class 10 Mathematics Board Paper Set 1 2018 (main)

    CBSE Class 10 Mathematics Marking Scheme Board Set 1 2018 (main)

  4. CBSE Class 10 Mathematics Board Paper Set 1 2018 (comp)

    CBSE Class 10 Mathematics Marking Scheme Board Set 1 2018 (comp)

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CLASS 10 SCIENCE

  1. CBSE Class 10 Science Sample Paper 2018-19

    CBSE Class 10 Science Marking Scheme 2018-19

  2. CBSE Class 10 Science Sample Paper 2017-18

    CBSE Class 10 Science Marking Scheme 2017-18

  3. CBSE Class 10 Science Board Paper Set 1 2018 (main)

    CBSE Class 10 Science Marking Scheme Board Paper Set 1 2018 (main)

  4. CBSE Class 10 Science Board Paper Set 1 2018 (comp)

    CBSE Class 10 Science Marking Scheme Board Paper Set 1 2018 (comp)

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CLASS 12 MATHEMATICS

  1. CBSE Class 12 Mathematics Sample Paper 2018-19

    CBSE Class 12 Mathematics Marking Scheme 2018-19

  2. CBSE Class 12 Mathematics Sample Paper 2017-18

    CBSE Class 12 Mathematics Marking Scheme 2017-18

  3. CBSE Class 12 Mathematics Board Paper (main) 2018

    CBSE Class 12 Mathematics Board Paper Marking Scheme(main) 2018

  4. CBSE Class 12 Mathematics Board Paper (main) 2017

    CBSE Class 12 Mathematics Board Paper Marking Scheme(main) 2017

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CLASS 12 PHYSICS

  1. CBSE Class 12 Physics Sample Paper 2018-19

    CBSE Class 12 Physics Marking Scheme 2018-19

  2. CBSE Class 12 Physics Sample Paper 2017-18

    CBSE Class 12 Physics Marking Scheme 2017-18

  3. CBSE Class 12 Physics Board Paper 2018 (main) Set-2
  4. CBSE Class 12 Physics Marking Scheme Board Paper 2018 (main) Set-2

  5. CBSE Class 12 Physics Board Paper 2017 (main) Set-1
  6. CBSE Class 12 Physics Marking Scheme Board Paper 2017 (main) Set-1

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CLASS 12 CHEMISTRY

  1. CBSE Class 12 Chemistry Sample Paper 2018-19

    CBSE Class 12 Chemistry Marking Scheme 2018-19

  2. CBSE Class 12 Chemistry Sample Paper 2017-18

    CBSE Class 12 Chemistry Marking Scheme 2017-18

  3. CBSE Class 12 Chemistry Board Paper (main) 2018

    CBSE Class 12 Chemistry Board Paper (main) 2018

  4. CBSE Class 12 Chemistry Board Paper (main) 2017

    CBSE Class 12 Chemistry Board Paper (main) 2017

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CLASS 12 ECONOMICS

  1. CBSE Class 12 Economics Sample Paper 2018-19

    CBSE Class 12 Economics Marking Scheme 2018-19

  2. CBSE Class 12 Economics Sample Paper 2017-18

    CBSE Class 12 Economics Marking Scheme 2017-18

  3. CBSE Class 12 Economics Board Paper (main) 2018

    CBSE Class 12 Economics Marking Scheme Board Paper (main) 2018

  4. CBSE Class 12 Economics Board Paper (main) 2017

    CBSE Class 12 Economics Marking Scheme Board Paper (main) 2017

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CLASS 11 MATHEMATICS

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CLASS 11 PHYSICS

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CLASS 11 CHEMISTRY

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CLASS 11 ECONOMICS

READERS' QUESTIONS

Q: A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the Sun = 2 × 1030 kg; mass of mars = 6.4 × 1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 × 108 kg; G= 6.67 × 10–11 N m2 kg–2.

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Answer:

Given,

Mass of the spaceship, m = 1000 kg

Mass of the Sun, MS = 2 × 1030 kg

Mass of Mars, MM = 6.4 × 1023 kg

Orbital radius of Mars, R = 2.28 × 108 km =2.28 × 1011 m

Radius of Mars, r = 3395 km = 3.395 × 106 m

Universal gravitational constant, G= 6.67 × 10–11 N m2 kg–2

Potential energy of the spaceship due to the gravitational attraction of the Sun

VS=- GMS mR

Potential energy of the spaceship due to the gravitational attraction of Mars

VM=- GMM mr

Since, the spaceship is stationed on Mars, its velocity and hence, its kinetic energy will be zero.

Therefore, total energy of the spaceship

V=VS+VM==- GMS mR- GMM mr=- GmMSR+MMr

The negative sign indicates that the system is in bound state.

Energy required for launching the spaceship out of the solar system

=  (Total energy of the spaceship)

= GmMSR+MMr

=6.67 ×1011×1000×2 × 10302.28 × 1011 +6.4 × 10233.395 × 106

=6.67 ×108×87.72 × 1017+1.88 × 1017

=6.67 ×108×89.50 × 1017

=598× 109 J

 6× 1011 J

Q: An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 N C−1 in Millikan’s oil drop experiment. The density of the oil is 1.26 g cm−3. Estimate the radius of the drop. (g = 9.81 m s−2; e = 1.60 × 10−19 C).

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Answer:

Since the drop is stationary, force (FE) due to electric field E is equal to the weight of the oil drop (W)

Let the radius of the oil drop be r

Mass of the oil drop m = Volume of the drop × Density of oil

m =43πr3×ρ 

W=mg=43πr3×ρ×g  

Electrostatic Force FE = qE

Excess electrons on an oil drop, n = 12

Charge on an electron, e = 1.6 × 10−19 C

q = Net charge on the oil drop = n e

= 12 × 1.6 × 10−19 C

Electric field intensity, E = 2.55 × 104 N C−1

Density of oil, ρ = 1.26 gm/cm3 = 1.26×103 kg/m3

Acceleration due to gravity, g = 9.81 m s−2

Putting the values in

E n e=43πr3×ρ×g 

r=3Ene4πρg3

=3×2.55×104×12×1.6×10-194×3.14×1.26×103×9.813

=946.09×10-213=9.82×10-7 m