Motion in A Plane

  • Question 1
    CBSEENBI11019949

    A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone. 

    Solution

    Given, 
    Length of the string, l = 80 cm
    Number of revolutions = 14
    Time taken = 25 s
    Frequency comma space straight nu space equals space fraction numerator No. space of space revolutions over denominator Time space taken end fraction space equals space 14 over 25

Angular space frequency comma space straight omega space equals space 2 πν space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 cross times 22 over 7 cross times 14 over 25
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 88 over 25 space rad divided by sec space

Centripetal space acceleration comma space straight a subscript straight c space equals space straight omega squared straight r space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses 88 over 25 close parentheses squared cross times 0.85 space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 9.91 space straight m divided by straight s squared space

    The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.

    Question 2
    CBSEENPH110024934

    Explain and derive parallelogram law of vector additor.

    Solution

    The parallelogram law of vector addition states that if two vectorsare represented by the two adjacent sides of a parallelogram by both magnitude and direction from a point, then their resultant can be represented by the diagonal of the parallelogramfrom the same point.

    Question 3
    CBSEENPH110024935

    A projectile is thrown at an angle θ from the horizontal with velocity u under the gravitation field of the earth. Derive expressions for its:
    a)Time of its flight
    b)Height
    c)Horizontal Range

    Solution


    Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u .

    The point O is called the point of projection, θ is the angle of projection and OB = horizontal range. The total time taken by the particle from reaching O to B is called the time of flight.

    Now,

    (a). The total time of flight is

    Resultant displacement is zero in Vertical direction.

    Therefore, by using equation of motion

    s = ut-12gt2gt=2 sin θt = 2 sin θg

    (b). The  horizontal range is

    Horizontal range OA = horizontal component of velocity × total flight time

    R =u cos θ × 2u sin θgR = u2 sin 2θg

    (c). The maximum height is

    It is the highest point of the trajectory point A. When the ball is at point A, the vertical component of the velocity will be zero.

    By using equation of motion

    v2=u2 -2as0 = u2sin2θ-2gHH= u2sin2θ2g

    Hence, this is the required solution

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    Question 4
    CBSEENPH11017861

    What is a scalar quantity?

    Solution
    A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

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