$Assertion :$ $A$ thin stainless steel needle can float on a still water surface.
$Reason :$ Any object floats when the buoyancy force balances the weight of the object.

  • A
    If both $Assertion$ and $Reason$ are correct and the $Reason$ is a correct explanation of the $Assertion$.
  • B
    If both $Assertion$ and $Reason$ are correct but $Reason$ is not a correct explanation of the $Assertion$.
  • C
    If the $Assertion$ is correct but $Reason$ is incorrect.
  • D
    If both the $Assertion$ and $Reason$ are incorrect.

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$A$ balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it,its radius changes from $R$ to $0$ in time $T$. If the speed $\psi(r)$ of gas coming out of the balloon depends on $r$ as $r^\alpha$ and $T \propto S^a A^\beta \rho^\gamma R^\delta$,then:

Match column-$I$ with column-$II$.
Column-$I$ Column-$II$
$(A)$ Hydraulic lift $(P)$ Archimedes' principle
$(B)$ Razor blade can be made to float on the surface of water $(Q)$ Pascal's law
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$(D)$ Ship is floating on the ocean $(S)$ Pressure

Which of the following is not the property of an ideal fluid?

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