Laws of Motion

Question 585
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 586
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 587
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

Question 588
CBSEENPH11026403

Assertion:  Pseudo force is an imaginary force which is recognised only by a non-inertial observer to explain the physical situation according to Newton's laws.

Reason: Pseudo force has no physical origin, i.e., it is not caused by one of the basic interactions in nature. It does not exist in the action-reaction pair.

  • If both assertion and reason are true and reason is the correct explanation of assertion.

  • If both assertion and reason are true but reason is not the correct explanation of assertion.

  • If assertion is true but reason is false.

  • If both assertion and reason are false.

Solution

B.

If both assertion and reason are true but reason is not the correct explanation of assertion.

Pseudo force is an imaginary force which is recognised only by a non-inertial observer to explain the physical situation according to Newton's laws. The magnitude of this force F is equal to the mass m of the object and acceleration α of the frame of reference. The direction of force is opposite to the direction of acceleration.

      F = - m α

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