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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by
  • A
    $2\pi \sqrt {\frac{{M\eta }}{L}} $
  • B
    $2\pi \sqrt {\frac{L}{{M\eta }}} $
  • C
    $2\pi \sqrt {\frac{{ML}}{\eta }} $
  • ✓
    $2\pi \sqrt {\frac{M}{{\eta L}}} $
✓

Answer

Correct option: D.
$2\pi \sqrt {\frac{M}{{\eta L}}} $
d
(d) By substituting the dimensions of mass $[M]$, length $[L] $ and coefficient of rigidity $\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]$ we get $T = 2\pi \sqrt {\frac{M}{{\eta L}}} $ is the right formula for time period of oscillations

$(a, b, c)$ Reynolds number and coefficient of friction are dimensionless.

Latent heat and gravitational potential both have dimension $[{L^2}{T^{ - 2}}]$.

Curie and frequency of a light wave both have dimension $[{T^{ - 1}}]$.

But dimensions of Planck's constant is $[M{L^2}{T^{ - 1}}]$ and torque is $\left[ {M{L^2}{T^{ - 2}}} \right]$

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