Basic physics units problems involving the Ideal Gas Law

[jamiebean]

Homework Statement

The following is the equation of ideal gas law, where p is pressure (Force/Area), V is volume, n is number of moles and T is temperature in Kelvin. What is the fundamental unit of R?
pV = nRT
A. kg^−1 · m^−2 · s^ 2 · K · mol
B. kg^−1 · m^−4 · s ^2 · K · mol
C. kg · m^4 · s ^−2 · K · mol^−1
D. kg · m^2 · s ^−2 · K^−1 · mol^−1
E. R is dimensionless

The fundamental unit of acceleration a is ms^−2 . Which of the following equations is/are impossible? Give a brief justification. (t is time, v is velocity and A, B and C are dimensionless constants)
A. a = A^−2BC^4 + v /t
B. a = Cv /t
C. a = v /t
D. a = v/ t ^2
E. a = t + v /t

Which of the following is the typical mass (60 g) of a tennis ball?
A. 6 × 10^4 mg
B. 60 × 10^−1 kg
C. 600 × 10^5 µg
D. 6000 × 10^−5 g
E. 60 000 × 10^5 ng

Homework Equations

The Attempt at a Solution

3:
I both calculated 60g in choice A and C
but there should only be 1 answer in this q. idk what happened.

2,1: because I am a starter, i have no idea how things work in these 2 q.

 

[kuruman]

Your calculations in 3 are correct. Both A and C amount to 60 g.

2,1: because I am a starter, i have no idea how things work in these 2 q.

I cannot interpret this. Can you translate in plain English?

 

[jamiebean]

Your calculations in 3 are correct. Both A and C amount to 60 g.

I cannot interpret this. Can you translate in plain English?

sorry for my bad eng. in other words, i don't know how to calculate question 1 and 2.

 

[kuruman]

Are you familiar with dimensional analysis? Most textbooks deal with it in chapter 1. Read your textbook about it and see here for another example
https://www.physics.uoguelph.ca/tutorials/dimanaly/

 

[jamiebean]

Are you familiar with dimensional analysis? Most textbooks deal with it in chapter 1. Read your textbook about it and see here for another example
https://www.physics.uoguelph.ca/tutorials/dimanaly/

in q2,choice B and C are possible. But I am not sure if choiceA,D,E are possible or not

 

[gneill]

in q2,choice B and C are possible. But I am not sure if choiceA,D,E are possible or not

Can you state the reasoning you've used (so far) to reach the above conclusions?
What rules of dimensional analysis have you invoked?