# If young modulus of a metal is 10^10 N/m^2, express it in a new system of units where the units of mass, length and time are 10 g, 100 cm, and 1/10 sec respectively.

Ramesh V
70 Points
14 years ago

the dimensional formula of Youngs modulus is ML-1T-2 with units as N/m2

ML-1T-2 here M in kgs, L in meters, T in secs

which is 1000grams/[100 cms*(10*10-1)2 secs2]

in terms of 10 g, 100 cm, and 1/10 sec respectively we have

100*(10 grams) / (100 cms) * 100*(1/10 sec)2

so Youngs modulus of metal is 10^10 [(10 grams) / (100 cms)*(1/10 sec)2]

8 Points
14 years ago

the old unit for young's modulus is N/m^2.=>Kg.m/s^(-2).1/m^2

=>kg.m^(-1).s^(-2)

=>1000g.(100cm)^(-1).(10.(1/10)s)^(-2)

=>100.10g.(100cm)^(-1).(1/100).(1/10)s)^(-2)

=>100.(1/100).[10g.(100cm)^(-1).(1/10)s)^(-2)]

=>new unit of youngs modulus

hence in new system also magnitude of youngs modulus is 10^10 new units.

10 Points
14 years ago

Hi

1N = 1 kg.m/s^2
= (1000 g)(100 cm) / (10 x 1/10 s)^2
= (100 x 10g)(1 x 100cm) / (100 x (1/10s)^2)        in this step we are trying to convert in the required system of units
= 1 (units of new system)
1m = 100 cm
= 1 (units of new system)

this implies 1 N/m^2 = 1 (units in new system)
Young's modulus in new system = 10^10 units

17 Points
14 years ago

Let the new units be

Dg = 10 g

m = 100 cm (is the same as meter) , and

ds = 1/10 s

Now, 1 N = 1 kg. m/s2

So we can write 1010 N/m2 as

1010 kg m/(m2s2) = 1010 kg/(ms2

Now we use two key ideas:

1. Multiplying by 1 does not make any difference

2. Since 1 kg = 1000 g, we can also say that (1000g/1 kg) , or (100 Dg/1 kg) = 1

Similary,

(1 s/10 ds)  = 1.

Squaring both sides, we get

(1 s2/100 ds2) = 1

Hence, 1010 kg/(ms2) = ( 1010 kg/ms2 )(1 s2/100 ds2) (100 Dg/1 kg)

= 1010 Dg/(m(ds)2) (cancelling out kg and s2)