Question

find the value of a force 100 dyne on a system based on meter, kilogram and minute as fundamental units? Solve by dimensional analysis

Answer 1

f=[mlt^-2]
a=1 b=1 c=-1
u1=u2[m1/m2]^a. [l1/l2]^b[t1/t2]^ c
u1=10²[g/kg]¹ [cm/m]¹ [second/minute]^-2
=10² [g/10³] [cm/10²] [ second/ 60second]^-2
=10²[10^-3][10^-2] [60]²
10²×10^-3×10^-2×36×10²
36×10^-5×10⁴
36×10^-1
3.6

Answer 2

Answer:

The value of a force 100 dyne on a system based on meter, kilogram and minute is $3.6 kg m/m^{2}$.

Explanation:

Given that,

Force F = 100 dyne

We know that,

Unit of force is dyne and  in CGS and

Dimension formula of force is [MLT^{-2}]

$n_{1}u_{1}=n_{2}u_{2}$....(I)

Here, $u_{1}$=unit of force in C.G.S

$u_{2}$=unit of force in M.K.S

$n_{1}$=100

Now, put the value of u₁, u₂ and n₁ in equation (I)

$n_{2}=100(\dfrac{1 gm}{1 kg})(\dfrac{1 cm}{1}m)(\dfrac{1 sec}{1 m})^{-2}$

$n_{2}=100\times(\dfrac{1}{1000})(\dfrac{1}{100})(\dfrac{1}{3600})^{-2}$

$n_{2}=100\times\dfrac{1}{1000}\times\dfrac{1}{100}\times3600$

$n_{2}=3.6\ kgm/m^2$

Hence, The value of a force 100 dyne on a system based on meter, kilogram and minute is $3.6 kg m/m^{2}$.