Unit measurement and dimensional analysis

You know 1000 mg = 1 g.  Convert 2.5 grams into milligrams.

• 25 mg
• 25,000 mg
• 250 mg
• 2500 mg

You know that 12 inches = 1 foot.  Convert 60 inches to feet.

• 720 feet
• 5 feet
• 5 inches
• 72 feet

10 mm=? nano meters

• 10⁴

• 10⁵

• 10⁶

• 10⁷

Dimensions of Torque (Torque=Force X Radius) is

• $MLT^{-2}$

• $ML^2T^{-1}$

• $ML^2T^{-3}$

• none of these

 $F=G\ \frac{m_{1\ }m_2}{r^2}$  
In this given equation the Dimensions of G are

•  $M^{-1}L^2T^{-2}$  

•  $M^{-1}L^3T^{-2}$  

•  $M^{-1}L^2T^2$  

• none of these

 $h=\frac{E}{\nu}\ \ where\ E\ is\ energy\ and\ \nu\ is\ frequency\ \left(\nu=\frac{1}{T}\ where\ T\ is\ time\right)$ Dimensions of h Planks constant is

•  $M^{ }L^2T^{-2}$  

•  $M^{ }L^{-2}T^{-2}$  

•  $M^{-1}L^2T^{-2}$  

•  $M^{ }L^2T^{-1}$  

Unit of angle in radians defined as arc length to radius is

•  $L^0$  

•  $L^2$  

•  $L$  

•  $L^{-1}$  

 $mass=\frac{X}{\sqrt{1-\frac{V^2}{C^2}}}\ \$  where V is velocity of the particle and C is speed of light. In this relation the Unit of X is

• Kg s / m

• kg m/s

• kg

• none of these