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Derive the following relation: alphaa=...

Derive the following relation:
`alpha_a=2alpha_l`

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Knowledge Check

  • A simple pendulum of length L and having a bob of mass M is oscillating in plane about a vertical line between angular limits -alpha and + alpha . At a time when the angular displacement is theta(lt alpha) , the tension in the string is T and the velocity of the bob is v. Which of the following relations will hold ?

    A
    `T cos theta = Mg`
    B
    `T - Mg cos theta = Mv^(2)//L`
    C
    The magnitude of the tangential acceleration of the bob is `|a_(r)| = g sin theta`
    D
    `T = mg cos theta`

  • If two rods of length L and 2L having coefficients of linear expansion alpha and 2 alpha respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composite rod equals

    A
    `(3)/(2) alpha`
    B
    `(5)/(2) alpha`
    C
    `(5)/(3) alpha`
    D
    None of these

  • If two rods of length L and 2L having coefficients of linear expansion alpha and 2alpha respectively are connected so that total length becomes 3L , the average coefficient of linear expansion of the composite rod equals

    A
    `(3)/(2)alpha`
    B
    `(5)/(2)alpha`
    C
    `(5)/(3)alpha`
    D
    None of these

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    If alpha and beta are the roots of the equation x ^(2) + alpha x + beta = 0, then

    Two rods of length L_(1) and L_(2) are made of materials whose coefficients of linear expansion are alpha_(1) and alpha_(2) . It the difference between the two lengths is independent of temperature, then

    A particle is moving along a circular pathh . The angular velocity , angular acceleration and centripetal acceleration of the particle at any instant respectively are vec(omega),vec(v),vec(alpha) and vec(alpha_(e )) . Which of the following relations is/are correct ?

    The distance between the points (a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a) 2|sin((alpha-beta)/(2))| b) 2|a sin((alpha-beta)/(2))| c) 2|a cos((alpha-beta)/(2))| d) |a cos((alpha-beta)/(2))|

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