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In a system of units, the unit of mass, length and timeare 1 quintal, 1 km and 1 h, respectively. In this system1 N force will be equal to :
  • a)
    1 new unit
  • b)
    129.6 new unit
  • c)
    125.7 new unit
  • d)
    103 new unit
Correct answer is option 'B'. Can you explain this answer?
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In a system of units, the unit of mass, length and timeare 1 quintal, ...
Given:

Unit of mass = 1 quintal = 100 kg

Unit of length = 1 km = 1000 m

Unit of time = 1 h

To find:

1 N force in this system of units.

Solution:

We know that force, F = ma, where m is the mass and a is the acceleration.

Also, we know that,

1 N = 1 kg m/s²

We can express the units of mass, length, and time in terms of standard units as follows:

1 quintal = 100 kg

1 km = 1000 m

1 h = 3600 s (since there are 60 minutes in an hour and 60 seconds in a minute)

Now, let's consider a body of mass 1 kg.

The weight of the body, W = mg, where g is the acceleration due to gravity.

In this system of units, the value of g is given by:

g = Gm/R²

where G is the gravitational constant, m is the mass of the earth, and R is the radius of the earth.

Substituting the values of G, m, and R, we get:

g = 9.81 m/s²

The weight of the body in this system of units is given by:

W = mg = 100 × 9.81 = 981 quintal m/s²

Now, let's calculate the acceleration produced by a force of 1 N on this body.

We know that,

F = ma

1 N = 1 kg m/s²

So,

a = F/m = 1/1 = 1 m/s²

Now, let's express this value in terms of the given units:

1 m/s² = 1/(1000/3600) km/h² = 1/(10/36) km/h² = 3.6 km/h²

Therefore,

1 N = 981 × 3.6 = 3523.6 new unit (approximately)

Hence, the correct option is B.
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In a system of units, the unit of mass, length and timeare 1 quintal, 1 km and 1 h, respectively. In this system1 N force will be equal to :a)1 new unitb)129.6 new unitc)125.7 new unitd)103 new unitCorrect answer is option 'B'. Can you explain this answer?
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