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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, ...
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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.
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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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? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 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? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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