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A rocket is fired from the earth towards...

A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravbitaional force on the rocket zero? Mass of the sun`=2xx10^(30)kg`, mass of the earth`=6xx10^(24)kg`. Neglect the effect of other planets etc. (orbital radius=`1.5xx10^(11)m`).

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To find the distance from the Earth's center where the gravitational force on the rocket is zero, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Variables**: - Let \( M_1 \) be the mass of the Sun: \( M_1 = 2 \times 10^{30} \, \text{kg} \) - Let \( M_2 \) be the mass of the Earth: \( M_2 = 6 \times 10^{24} \, \text{kg} \) - Let \( R \) be the distance from the Earth to the Sun: \( R = 1.5 \times 10^{11} \, \text{m} \) ...
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Knowledge Check

  • Choose the most appropriate option. A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre, the gravitational force on the rocket is zero? Mass of the Sun = 2 xx 10^(30) kg and mass of the Earth =6 xx 10^(24)kg .

    A
    `2.6 xx 10^(8)m`
    B
    `3.2 xx 10^(8)m`
    C
    `3.9 xx 10^(9)m`
    D
    `2.3 xx 10^(9)m`

  • A rocket is fired from the earth to the moon. The distance between the earth and the moon is r and the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero when its distance from the moon is

    A
    `(r)/(20)`
    B
    `(r)/(15)`
    C
    `(r)/(10)`
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    A
    `4.1xx10^(18)" N"`
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