Dimensions and consistency Quiz

1. What are the dimensions of power?

• A. $MLT^{-2}$
• B. $ML^{2}T^{-2}$
• C. $ML^{2}T^{-3}$
• D. $MLT^{-3}$

2. Which equation, with all letters having their usual meanings, is dimensionally consistent?

• A. $v=u+at^{2}$
• B. $s=ut+\frac12at^{2}$
• C. $F=mv$
• D. $E=mv$

3. The pressure $p$ in a fluid is $p=\rho gh$. What are the dimensions of $\rho gh$?

• A. $ML^{-1}T^{-2}$
• B. $MLT^{-2}$
• C. $ML^{-3}$
• D. $ML^{2}T^{-2}$

4. The speed $v$ of a wave on a string depends on tension $F$ and mass per unit length $\mu$, so $v=\lambda F^{a}\mu^{b}$. Find $a$.

• A. $1$
• B. $-\frac12$
• C. $2$
• D. $\frac12$

5. A student writes $x=A\sin(\omega t)$ where $x$ is a displacement. What are the dimensions of $\omega$?

• A. $T^{-1}$
• B. $T$
• C. $L$
• D. Dimensionless