Laws of Motion

  • Question 593
    CBSEENPH11026350

    A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is

    • 13 g

    • 9 g

    • 22 g

    • 12 g

    Solution

    D.

    12 g

    Consider the diagram in balance

           

             8x = wy

    ⇒        xy = w8                       ...(i)

    Also,  wx = 18 y

    ⇒         xy = 18w                     ....(ii)

    Dividing Eq. (i) and Eq. (ii) we get

                xyxy = w818w

    ⇒         1 = w218 × 8

    ⇒          w = 18 × 8

                 w = 12 g

    Question 594
    CBSEENPH11026352

    Universal time is based on

    • rotational effect of the earth about its axis

    • vibrations of cesium atom

    • orbital motion of the earth around the sun

    • oscillation of quartz crystal

    Solution

    A.

    rotational effect of the earth about its axis

    Time defined in terms of the rotation of the earth is called Universal Time (UT).

    Question 595
    CBSEENPH11026380

    A liquid of density 800  kg/m3 is filled in a cylindrical vessel upto a height of 3 m. This cylindrical vessel stands on a horizontal plane. There is a circular hole on the side of the vessel. What should be the minimum diameter of the hole to move the vessel on the
    floor, if plug is removed. Take the coefficient of friction between the bottom of the vessel and the plane as 0.5 and total mass of vessel plus vessel as 95 kg.

    • 0.107 m

    • 0.053 m

    • 0.206 m

    • 0.535 m

    Solution

    A.

    0.107 m

    Given:-

    ρ = 800 kg/m3

    h = 3 m

    μ = 0.5 

    m = 95 kg

    dmin = ?

        

    Let area of hole be a

    ∴ Reaction force F = ρ av2

                               = ρa. 2gh                            [v =2g h ]

     and fmax = μN

                   = μ mg

    μ= coefficient of friction

    ⇒          F ≥ fmax

    ⇒          2 ρ agh ≥ μ mg

    ⇒             a ≥ μ m2 ρ h

                    = 0.5 × 952 × 800 × 3

                a = 0.009

                 π r2 ≥ 0.009

                r ≥ 0.009π

            rmin ≥ 0.0535 m

         dmin = 2 rmin 

                 = 2 × 0.0535

         dmin = 0.107 m

    Question 596
    CBSEENPH11026399

    The figure shows a horizontal force F acting on a block of mass M on an inclined plane (angle θ).  What is the normal reaction N on the block?

         

    • mg sinθ + F cosθ

    • mg sinθ - Fcosθ

    • mg cosθ - F sinθ

    • mg cosθ + F sinθ

    Solution

    D.

    mg cosθ + F sinθ

      

    From the figure, the normal reaction on the block is

        N = mg cosθ + F sinθ

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