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29 April, 03:49

The acceleration (a) of a particle moving with uniform speed (v) in a circle of radius (r) is found to be propotional to r^n and v^m, where n and m are constants. Determine the values of n and m and write the simplest form of an equation of acceleration

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Answers (2)
  1. 29 April, 05:39
    0
    n=-1 and m=2

    Explanation:

    A particle is moving uniformly with acceleration "a"

    Uniform speed is v

    And radius of circle is r

    The acceleration is proportional to

    r^n and v^m

    i. e

    a∝ rⁿ

    a ∝v^m

    Combing the two

    Then, a∝rⁿv^m

    Let k be constant of proportionality

    Then, a=krⁿv^m. Equation 1

    So, we know that the centripetal acceleration keeping an object in circular path is given as

    a=v²/r

    Rearranging

    a=v²r^-1. Equation 2

    So comparing this to the proportional

    Equating equation 1 and 2

    krⁿv^m = v²r^-1

    This shows that,

    k=1

    rⁿ = r^-1

    Then, n = -1

    Also, v^m = v²

    Then, m=2

    Therefore,

    n=-1 and m=2
  2. 29 April, 07:35
    0
    m=2

    n = - 1

    a=Kv²/r

    Explanation:

    using dimensional analysis

    V = meter/second = m/s

    r = meter = m

    a = meter/second²=m/s²

    If a is proportional to r^n v^m

    we have a=r^n v^m = (m) ^n (m/s) ^m = m/s²

    from law of indices;

    m^n+m/s^m = m/s²

    using system of equations

    n+m=1

    m=2

    so n = - 1

    then a=kr^n v^m

    a=Kv²/r
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