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3 April, 03:07

Two objects a and b have the same size and shape, but a is twice as heavy as

b. when they are dropped simultaneously from a tower, they reach the ground at the same time. which has a greater momentum?

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Answers (2)
  1. 3 April, 05:07
    0
    In general momentum is defined as the product of mass and velocity. It is expressed as momentum (P) = mass (m in Kgs) * velocity (v in m/s) ie P = m * v kgm/s

    Given:

    Two objects of same size and shape a and b

    The velocity of the both the bodies are same ie velocity = v1 = v2=v - eqn 1 But they differ in heaviness as follows:

    The heaviness of the object a is two times of b

    ie a = 2b or a/b = 2 or a : b = 2 : 1

    mass of the body m1 = 2a - - eqn-2

    momentum of the body is a (P1) = 2m1 * v

    mass of the body m2 = b - - eqn 3

    momentum of the body b (P2) = m1 * v

    the momentum of the two bodies are P1 = P2

    ie m1*v1 = m2*v2

    P1 : P2 = m1*v1 : m2 * v2

    sub the value of v2, v1 from eqn 1, m1=2a, m2=b

    P1 : P2 = 2av : bv

    P1 : P2 = 2a : b

    ie (P1/P2) = (2a/b) - - eqn 4

    Ans : -

    from the above eqn 4 - it is obvious the momentum of body a is twice of body b

    ie momentum of the body a is greater.
  2. 3 April, 06:05
    0
    By definition we have that momentum is the product of the mass of the object by the velocity of the object. In other words:

    p = m * v

    Both objects have the same speed because they reach the ground at the same time.

    However, object a is heavier than object b. The weight of the objects is:

    a = 2m

    b = m

    Therefore the momentum of a and b is

    pa = 2mv

    pb = mv

    Object a has the greatest momentum

    Answer

    pa> pb

    2mv> mv
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