LATIHAN SOAL FISIKA SAT BESARAN DAN PENGUKURAN BAGIAN KEDUA

1. Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say r^n, and some power of v, say v^m, we write this acceleration a=k r^n v^m where k is a dimensionless constant. Determine the values of n and m?

1. -2 and 1

2. 1 and 2

3. -1 and 2

4. 2 and 1

5. 1 and -1

2. Which expression could be correct for the velocity v of ocean waves in terms of the density of sea-water, g the acceleration of free fall, h the depth of the ocean and the wavelength? 

   
   
   

3. Gravitational energy per unit mass V is given by the equation V=-GM/R where G, M, R represent gravitational constant, mass of planet and radius of planet respectively. The dimensions of G are.

   
   
   

4. The mass M of gas escaping in a short time t through a small hole of area A in the wall of a gas Cylinder is given by

   
   where C is constant, and P and are the pressure and density of the gas. Determined the values of the α, β, and γ

1. 1/2, 1/2, 1

2. 1/2, 1, 1/2

3. 1/2, -1/2, -1

4. -1/2, 1/2, 1

5. 1/2, 1/2, -1

5. Pressure in a gas filled container is given by the equation :P=(α+t^2)/βh where " α " and " β " are constant, ” t ”  is temperature and ” h ” is the height. Find the dimension of ratio " ".

   
   
   

6. It is observed that the velocity ‘ v ‘ of a liquid leaving a nozzle depends upon the pressure drop ‘ p ‘ and the density ‘ ρ ‘. The relationship between them is of the form ….

   
   
   

7. How many nanometers are in a kilometer ?

1. 10^-9

2. 10^9

3. 10^-12

4. 10^12

5. 10^27

8. Given the following equations :

   
   
   

Where v, x, ρ, η represent the speed of an object, width of the object, density of liquid, coefficient of viscosity of liquid ( unit : kg m^-1 s^-1 ) while A, B, and C are dimensionless constants. Determine which equation ( s ) is / are dimensionally correct.

1. (1)

2. (2)

3. (3)

4. (4)

5. (1) and (2)

9. It is observed that the frequency of oscillation of a guitar string ‘ f ‘ depends upon the mass ‘ m ‘, the length ‘ l ‘and tension ‘ F ‘. The relationship between them is….

   
   
   

10. The theory of gas flow through small diameter tubes at low pressures is an important consideration of high vacuum technique. One equation which occurs in the theory  

is

Where k is a number without units, r is the radius of the tube, P1 and P2 are the pressures at each end of the tube of length l, M is the molar mass of the gas ( unit : kg mol^-1 ), R is the molar gas constant ( unit : J K^-1 mol^-1 ) and T is the temperature. What are the dimensions of Q?

1. M T^-3

2. M T^-2

3. M T^-1

4. M T^-4

5. M T^-5

Sumber: soal soal Salim Sabtu 

Pembahasan:

1. 
   
   

Karena k adalah konstanta tak bersatuan maka k bisa diabaikan di perhitungan 

Sehingga rumusnya menjadi 

2. 
   
   

Sehingga persamaan dapat ditulis menjadi

3. 
   

   

Untuk analisis dimensi tanda minus dapat diabaikan 

4. 

Karena C adalah konstanta tak bersatuan maka kita bias abaikan di perhitungan ini 

Sehingga rumusnya menjadi 

5. 
   
   

Karena satuan α dengan t^2 pasti sama maka mereka bisa digabungkan 

6. 
   
   
   
   Sehingga rumusnya menjadi 

7.  1 nm=...km

8. 
   
   
   Sehingga rumusnya menjadi 

9. 
   
   

   
   
   Sehingga rumusnya menjadi 

10.