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With what minimum velocity v should a pa...

With what minimum velocity v should a particle be thrown horizontally from a height h above the surface of the earth of mass M so that it does not fall back on the earth ? Radius of earth is R ?

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AI Generated Solution

To solve the problem of finding the minimum velocity \( v \) with which a particle should be thrown horizontally from a height \( h \) above the surface of the Earth so that it does not fall back, we will derive the escape velocity for the particle at that height. ### Step-by-Step Solution: 1. **Understanding the Situation**: - We have a particle of mass \( m \) thrown horizontally from a height \( h \) above the Earth's surface. The radius of the Earth is \( R \) and its mass is \( M \). 2. **Determine the Effective Radius**: ...
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Knowledge Check

  • The escape velocity from the surface of the earth is (where R_(E) is the radius of the earth )

    A
    `sqrt(2gR_(E))`
    B
    `sqrt(gR_(E))`
    C
    `2sqrt(gR_(E))`
    D
    `sqrt(3gR_(E))`

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