Question 585

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

A liquid of density 800 kg/m^{3} 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/m^{3}

h = 3 m

μ = 0.5

m = 95 kg

d_{min} = ?

Let area of hole be a

∴ Reaction force F = ρ av^{2}

= ρa. 2gh [$\because $v =$\sqrt{2\mathrm{g}\mathrm{h}}$ ]

and f_{max} = μN

= μ mg

μ= coefficient of friction

⇒ F ≥ f_{max}

⇒ 2 ρ agh ≥ μ mg

⇒ a ≥ $\frac{\mathrm{\mu}\mathrm{m}}{2\mathrm{\rho}\mathrm{h}}$

= $\frac{0.5\times 95}{2\times 800\times 3}$

a = 0.009

$\mathrm{\pi}$ r^{2} ≥ 0.009

r ≥ $\sqrt{\frac{0.009}{\mathrm{\pi}}}$

r_{min} ≥ 0.0535 m

d_{min} = 2 r_{min}

= 2 × 0.0535

d_{min} = 0.107 m

Question 587

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

**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 = $-\mathrm{m}\mathrm{\alpha}$