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Solve the integral I=intoo^R(GMm)/(x^2)d...

Solve the integral `I=int_oo^R(GMm)/(x^2)dx`.

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`I=int_oo^R(GMm)/(x^2)dx=GMm int_oo^R(dx)/(x^2)=GMm[-1/x]_oo^R`
`=GMm[-1/R+1/oo]=(-GMm)/(R)`
The above expression represents gravitational potential energy which is obtained by integrating `GMm//x^2` between the limits infinity `(oo)` and radius of the earth (R).
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CENGAGE PHYSICS ENGLISH-BASIC MATHEMATICS-Exercise 2.6
  1. Solve the integral I=intoo^R(GMm)/(x^2)dx.

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  2. The displacement of a particle is given by y=(6t^2+3t+4)m, where t is ...

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  3. The velocity of a particle is given by v=12+3(t+7t^2). What is the acc...

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  4. A particle starts from origin with uniform acceleration. Its displacem...

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  5. The acceleration of a particle is given by a=t^3-3t^2+5, where a is in...

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  6. A particle starts moving along the x-axis from t=0, its position varyi...

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  7. A particle moves along the x-axis obeying the equation x=t(t-1)(t-2), ...

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  8. The speed of a car increases uniformly from zero to 10ms^-1 in 2s and ...

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  9. A car accelerates from rest with 2ms^-2 for 2s and then decelerates co...

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  10. A stationary particle of mass m=1.5kg is acted upon by a variable forc...

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  11. The displacement of a body at any time t after starting is given by s=...

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  12. A particle moves along a straight line such that its displacement at a...

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  13. The displacement x of a particle moving in one dimension under the act...

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  14. The position x of a particle varies with time t according to the relat...

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  15. The displacement of a particle along the x-axis is given by x=3+8t+7t^...

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  16. The acceleration a in ms^-2 of a particle is given by a=3t^2+2t+2, whe...

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  17. The displacement x of a particle along the x-axis at time t is given b...

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  18. A particle moves along a straight line such that its displacement at a...

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  19. The acceleration of a bus is given by ax(t)=at, where a=1.2ms^-2. If...

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  20. The acceleration of a motorcycle is given by ax(t)=At-Bt^2, where A=1....

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  21. The acceleration of a particle varies with time t seconds according to...

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