Maths

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A uniform cylindrical container is half filled with water. The height of the
cylinder is twice its diameter. The cylinder is gradually tilted until the water
touches the brim. At this instant, the container is inclined at which angle:
1.30
2.45
3.60
4.75
all to the vertical

  • Maths -

    Looking from the side, the cylinder has an outline of a rectangle, of height 2x and width x.

    Since the cylinder is half-filled, at the point water touches the brim, there is as much water in the cylinder as there is air. So the water level divides the cylinder into two equal parts.

    The final position of the cylinder is such that the diagonal is horizontal.

    The angle the diagonal makes with the vertical side is tan-1(1/2)=26.565 degrees.
    So the angle the axis of the cylinder makes with the vertical is 90-26.565=73.435 degrees, unfortunately it does not correspond to any one of the choices above.

    Anchal, could you check if there is a typo in the question?

  • Maths -

    It is given that height of the cylinder is twice that of its diameter. Using this we can imagine that when we tilt the cylinder until the water touches the brim, the height falls to half of its original height. Using formula
    Sin x = p/h
    Where, p = h/2 = D
    and h= 2D
    We get, sin x = 1/2
    x = 30 degree

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