Questions about Chapter 1: Measurement.

Question 1:

**A
pipe delivers 600 gallons of water per minute.
How long does it take to fill a swimming pool having a rectangular base
of 10 m x 10 m and a depth of 2 m ? Give your answer in minutes. [ 1
Gallon = 3.79 liters ; 1 liter = 1000 cm ^{3}
]
**

Question
2: **
**

**Force
is a physical quantity with dimensions equal to the dimension of mass
multiplied by the dimension of acceleration.
Suppose the force acting on an object is given by
**

**
****F
= K m ^{a} v^{b} x^{c}
,**

**where
m, v and x have the dimensions of mass, velocity and distance, respectively.
K is a dimensionless constant. Use dimensional analysis to find the numerical values of the
constants a, b and c.
**

**ANS:
a =
1 ;
b =
2 ;
c =
-1.**

Question
3: **
**

Assume
the density of nitrogen gas, r
, in a container that measures 1.0mx2.0mx4.0m
is 1/800 that of water, and r** (
water ) = 1.0 g/cm ^{3}.
Find the number of nitrogen molecules in the container, given that the
molecular weight of nitrogen
M = 28 g and Avogadro’s number is N_{A} = 6.02x10^{23}
molecules/mole.**

**ANS:
2.15x10 ^{26} molecules.
**

Question
4: **
**

**The
acceleration “ a ” of a particle is given by the following equation
**

**
a = B v ^{2} + ( s C ) / t^{2}**

**where
v is the velocity, t is the time and s is the displacement.
Determine the dimensions of B and C.**

**ANS: ****
****unit
of ****B****
**is**
****1****/****m****
****a****n****d****
****C****
**is
dimensionless**.**