Match the entries in List-$I$ with those in List-$II$.
$A$. Unified interaction reducing the number of fundamental forces from four to three$(i)$ Strong interaction
$B$. Force between two molecules separated by a distance near about the sum of the molecular radii$(ii)$ Gravitational force
$C$. Nuclear binding force$(iii)$ Electroweak interaction
$D$. Bodies of astronomical proportions$(iv)$ Electromagnetic interaction

  • A
  • B
  • C
  • D

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The length of a cylinder is measured with a meter rod having a least count of $0.1 \, cm$. Its diameter is measured with vernier calipers having a least count of $0.01 \, cm$. Given that the length is $5.0 \, cm$ and the radius is $2.0 \, cm$,the percentage error in the calculated value of the volume will be ......... $\%$

Estimate the average mass density of a sodium atom assuming its size to be about $2.5 \; \mathring{A}$. (Use the known values of Avogadro's number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: $970 \; kg \; m^{-3}$. Are the two densities of the same order of magnitude? If so,why?

The quantities which have the same dimensions as those of solid angle are:

Which of the following has the same dimensional formula?

Match List-$I$ and List-$II$:
List-$I$ List-$II$
$A$. Young's Modulus $(Y)$ $I$. $[M L^{-1} T^{-1}]$
$B$. Co-efficient of Viscosity $(\eta)$ $II$. $[M L^2 T^{-1}]$
$C$. Planck's Constant $(h)$ $III$. $[M L^{-1} T^{-2}]$
$D$. Work Function $(\varphi)$ $IV$. $[M L^2 T^{-2}]$

Choose the correct answer from the options given below:

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