MEASUREMENTS

 $P=\frac{\alpha}{\beta}e^{-\frac{az}{k\theta}}$  
The variation of pressure P with distance z is given by the above expression.
where  $\alpha,\beta\$  are constants, k is Boltzmann constant and
 $\theta$  is temperature. The dimensional formula of  $\beta$  will be_______ 

•  $\left[M^{-1}L\ T^2\right]$  

•  $\left[M^0L^0T^0\right]$  

•  $\left[M^0L^2T^0\right]$  

•  $\left[M^1L^{-1}T^{-2}\right]$  

If the force (F), velocity (V) and time (T) are chosen as the fundamental units, the dimensions of mass are:

• $\left[FVT^{-1}\right]$

• $\left[FVT^{-2}\right]$

• $\left[FV^{-1}T^{-1}\right]$

• $\left[FV^{-1}T\right]$

The dimensional formula for energy E is

• $\left[ML^2T^{-2}\right]$

• $\left[ML^{ }T^{-2}\right]$

• $\left[ML^2T^{ }\right]$

• $\left[L^2T^{-2}\right]$

Find the dimensions of a/b in the relation

 $F\ =\ a\sqrt{x}\ +\ bt^2$  
where F is force, x is distance and t is time

•  $\left[L^{ }T^2\right]$  

•  $\left[L^{-\frac{1}{2}}T\right]$  

•  $\left[L^{-1}T^2\right]$  

•  $\left[L^{-\frac{1}{2}}T^2\right]$  

 $X\ =\ A\ +\ vt$  
In the above expression X is distance, v is velocity and t is time. The dimensions of A will be equivalent to ________

• time

• velocity

• distance

• none of the options

Find the result of 12.637- 2.42 with proper significant figures

• 10.217

• 10.2

• 10.22

• 10

Find the result of 46.75/1.3 with proper significant figures

• 35.96

• 36

• 35.9

• 35.961

Round off the below number up to 4 digits

377234

• 377200

• 377.222

• 377

• 30000

A physical quantity is x is given by 

 $x\ =\ a^2\times b^2$  
If the percentage errors of a and b are 3% and 1% respectively then calculate the percentage error in the calculation of x

• 9%

• 6%

• 8%

• 7%

If the time period of a pendulum is measured as 2.1 s, 2.2 s, 2.1 s and 2.2 s. The mean absolute error will be

• 0.15

• 0.05

• 0.1

• 2.15