Match List $I$ with List $II$
LIST$-I$ | LIST$-II$ |
$(A)$ Torque | $(I)$ $ML ^{-2} T ^{-2}$ |
$(B)$ Stress | $(II)$ $ML ^2 T ^{-2}$ |
$(C)$ Pressure of gradient | $(III)$ $ML ^{-1} T ^{-1}$ |
$(D)$ Coefficient of viscosity | $(IV)$ $ML ^{-1} T ^{-2}$ |
Choose the correct answer from the options given below
$(A)-(III), (B)-(IV), (C)-(I), (D)-(II)$
$(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
$(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$
$(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$
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.
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula
The formula $X = 5YZ^2$, $X$ and $Z$ have dimensions of capacitance and magnetic field respectively. What are the dimensions of $Y$ in $SI$ units?