Units and Measurements - Online Test

Answer : Option C
Explaination / Solution:

Principle of homogenity of dimensions states that “For an equation to be dimansionally correct, the dimensions of each term on LHS must be equal to the dimensions of each term on RHS.”

Answer : Option C
Explaination / Solution:

Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique. Another use of dimensional analysis is in checking the correctness of an equation which you have derived after some algebraic manipulation. Even a minor error in algebra can be detected because it will often result in an equation which is dimensionally incorrect.

Answer : Option D
Explaination / Solution:

if an equation fails this consistency test, it is proved wrong, but if it passes, it is not proved right. Thus, a dimensionally correct equation need not be actually an exact (correct) equation, but a dimensionally wrong (incorrect) or inconsistent equation is definitely wrong.

Answer : Option B
Explaination / Solution:

The SI derived unit of electric charge is the coulomb (C). The symbol Q often denotes charge.

Answer : Option A
Explaination / Solution:

Pressure is not the same physical thing as stress, but they do use the same definition and thus produce the same units, so the same calculator can be used for both. They both measure force per unit area. SI unit of both pressure and stress is Pascal.

Answer : Option D
Explaination / Solution:

Side of cube (a) = 2 cm  = 2×10−2m

Volume of cube (V) = a3=(2×10−2)3

= 8.0×10−6m3

Answer : Option B
Explaination / Solution:

Radius of cylinder r = 2 cm = 20 mm

Height of cylinder h = 10 cm = 100 mm

Surface area of cylinder = 2πr(r+h)

= 2×3.14×20(20+100)

= 2×3.14×20×120

= 15072 mm​​​​​2

 ≈1.5×104mm2

Answer : Option C
Explaination / Solution:

Speed of vehicle = 18 km h​​​​​​-1

Mean it cover 18 km in 1 hour {3600 seconds)

Distance covered in 3600 sec = 18km = 18000 m

Distance covered in 1 sec = 180003600=5m

Answer : Option B
Explaination / Solution:

Relative density means how much times a substance is denser than water.

Now relative density of lead = 11.3 means lead is 11.3 times denser than water.

Now water has a density 1 g cm–3 in cgs units

Thus lead will have a density =  11.3 x 1 g cm–3 = 11.3 g cm–3

Answer : Option A
Explaination / Solution:

We know 1 kg = 103 g

1 m​​​​​​2 = 104 cm

1 s​​​​​​-2 = 1s-2

​​​​​​multiply all these quantities we get

=> 1 kg m​​​​​​2 s​​​​​​-2  = 103×104gcm2s−2

=>1kgm2s−2=107gcm2s−2