The decimal point is placed after two digits starting from the end. For each decimal place, we can write the number divided by 100.
21.12 can be written as 
.
Divide the numerator and denominator by 2:
The numerator and denominator can be divided by 2 again:
There is no other common factor between numerator and denominator other than 1. Hence, it is the reduced form.
Answer:
As the concentration of a solute in a solution increases, the freezing point of the solution <u><em>decrease </em></u>and the vapor pressure of the solution <em><u>decrease </u></em>.
Explanation:
Depression in freezing point :
where,
=depression in freezing point =
= freezing point constant
m = molality ( moles per kg of solvent) of the solution
As we can see that from the formula that higher the molality of the solution is directly proportionate to the depression in freezing point which means that:
- If molality of the solution in high the depression in freezing point of the solution will be more.
- If molality of the solution in low the depression in freezing point of teh solution will be lower .
Relative lowering in vapor pressure of the solution is given by :
= Vapor pressure of pure solvent
= Vapor pressure of solution
= Mole fraction of solute
Vapor pressure of the solution is inversely proportional to the mole fraction of solute.
- Higher the concentration of solute more will the be solute's mole fraction and decrease in vapor pressure of the solution will be observed.
- lower the concentration of solute more will the be solute's mole fraction and increase in vapor pressure of the solution will be observed.
Answer:
0.893 rad/s in the clockwise direction
Explanation:
From the law of conservation of angular momentum,
angular momentum before impact = angular momentum after impact
L₁ = L₂
L₁ = angular momentum of bullet = + 9 kgm²/s (it is positive since the bullet tends to rotate in a clockwise direction from left to right)
L₂ = angular momentum of cylinder and angular momentum of bullet after collision.
L₂ = (I₁ + I₂)ω where I₁ = rotational inertia of cylinder = 1/2MR² where M = mass of cylinder = 5 kg and R = radius of cylinder = 2 m, I₂ = rotational inertia of bullet about axis of cylinder after collision = mR² where m = mass of bullet = 0.02 kg and R = radius of cylinder = 2m and ω = angular velocity of system after collision
So,
L₁ = L₂
L₁ = (I₁ + I₂)ω
ω = L₁/(I₁ + I₂)
ω = L₁/(1/2MR² + mR²)
ω = L₁/(1/2M + m)R²
substituting the values of the variables into the equation, we have
ω = L₁/(1/2M + m)R²
ω = + 9 kgm²/s/(1/2 × 5 kg + 0.02 kg)(2 m)²
ω = + 9 kgm²/s/(2.5 kg + 0.02 kg)(4 m²)
ω = + 9 kgm²/s/(2.52 kg)(4 m²)
ω = +9 kgm²/s/10.08 kgm²
ω = + 0.893 rad/s
The angular velocity of the cylinder bullet system is 0.893 rad/s in the clockwise direction-since it is positive.
Answer:
v = 21.25 km/h
The average velocity is 21.25km/h
Explanation:
Average velocity = total displacement/time taken
v = d/t
Given;
A car travels 50 km in 25 km /h
d1 = 50km
v1 = 25km/h
time taken = distance/velocity
t1 = d1/v1
t1 = 50/25 = 2 hours
and then travels 60km with a velocity 20 km/h
d2 = 60km
v2 = 20km/h
t2 = d2/v2 = 60/20
t2 = 3 hours
and then travels 60km with a velocity 20 km/h in the same direction
d3 = 60km
v3 = 20km/h
t3 = d3/v3 = 60/20
t3 = 3 hours
Average velocity = total displacement/total time taken
v = (d1+d2+d3)/(t1+t2+t3)
v = (50+60+60)/(2+3+3)
v = 170/8
v = 21.25 km/h
The average velocity is 21.25km/h
