Match List $I$ with List $II$
List $I$ | List $II$ |
$A$ Spring constant | $I$ $(T ^{-1})$ |
$B$ Angular speed | $II$ $(MT ^{-2})$ |
$C$ Angular momentum | $III$ $(ML ^2)$ |
$D$ Moment of Inertia | $IV$ $(ML ^2 T ^{-1})$ |
Choose the correct answer from the options given below
$(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$
$(A)-(IV), (B)-(I), (C)-(III), (D)-(II)$
$(A)-(II), (B)-(III), (C)-(I), (D)-(IV)$
$(A)-(I), (B)-(III), (C)-(II), (D)-(IV)$
The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
The dimension of the ratio of magnetic flux and the resistance is equal to that of :
If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$
$(b)\;y=a \sin v t$
$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.