1. The equation (p+a/V

^{2 }) (V-b)= constant. The units of a is ?^{5}

^{4}

^{3}

^{2}

According to the principle of dimensional homogenity [P]=[a/V

^{2}]”

=> [a] = [P][V

^{2}] = [ML

^{-1}T

^{-2}] [L

^{6}] = [ML

^{5}T

^{-2}]

or unit of a = gm × cm

^{5}× sec

^{-2}= Dyne × cm

^{4}

2. If x = at + bt

^{2}where x is the distance travelled by the body in kilometre while t the time in seconds, then the units of b are ?^{2}

^{2}

From the principle of dimensional homogenity [x] = [bt

^{2}] => [b] = [x/t

^{2}]

So Unit of b = km/s

^{2}

3. The unit of absolute permittivity is ?

^{2}

^{2}

^{2}

4. Unit of Stefan’s constant is ?

^{-1}

^{-2}s

^{-1}K

^{-4}

^{-2}

^{2}

^{2}

5. The unit of surface tension in SI system is ?

^{2}

^{2}

^{2}

6. A suitable unit for gravitational constant is ?

^{-2}

^{-2}sec

^{2 kg -2}

^{-2}

7. The SI unit of universal gas constant (R) is ?

^{-1}mol

^{-1}

^{-1}mol

^{-1}

^{-1}mol

^{-1}

^{-1}mol

^{-1}

8. X = 3YZ

^{2}find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively ?^{-3}L

^{-2}T

^{-4}A

^{-1}

^{-2}

^{-3}L

^{-2}T

^{4}A

^{4}

^{-3}L

^{-2}T

^{8}A

^{4}

9. If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula
for C

^{2}LR is ?^{-2}T

^{-1}I

^{0}]

^{0}L

^{0}T

^{3}I

^{0}]

^{-1}L

^{-2}T

^{6}I

^{2}]

^{0}L

^{0}T

^{2}I

^{0}]

10. A force F is given by F = at + bt

^{2}, where t is time. What are the dimensions of a and b ?^{-3}and ML

^{2}T

^{-4}

^{-3}and ML T

^{-4}

^{-1}and ML T

^{0}

^{-4}and ML T

^{1}