The Question is from neet-physics units-and-measurement priniciple-of-homoginity, and it was created by the author ABDUL JILANI BASHA

Question

What will be the unit of time in that system in which the unit of length is metre, unit of mass is kg and unit of force is kg wt?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Relationship between force, mass, and acceleration.
	**Related Topics**: Units and Dimensions, Newton's Second Law of Motion.
	**Prerequisites**: Understanding of force as mass times acceleration, and dimensional analysis.
## SOLUTION PATHWAY
**Given Information**:
	Unit of length: metre (m)
	Unit of mass: kilogram (kg)
	Unit of force: kg weight (kg wt)
	kg wt = g * kg, where g = 9.8 m/s²
**Method & Steps**:
	1. Express force in terms of mass, length, and time:
		Reasoning: Force (F) = mass (m) × acceleration (a). Acceleration is length (L) per time (T) squared (a = L/T²).
		Formula/Rule:  F = ma = m(L/T²)
	2.  Express the given unit of force (kg wt) in base units:
		Working: kg wt = kg * g, where g is acceleration due to gravity (9.8 m/s²). Therefore, kg wt in terms of base units is kg * m/s²
		Key Point:  kg wt represents a force equal to the weight of a 1 kg mass, which is mass times the acceleration due to gravity.
	3. Equate the two expressions for force and solve for the time unit:
		Working:  kg * m/s² = m * L/T²  =>  kg * 9.8 m/s² = kg * (m/T²),  9.8 m/s² = m/T²,  T² = 1/9.8  => T = 1/sqrt(9.8) s
		Result: The unit of time is 1/sqrt(9.8) seconds.
		Verification: The derived time unit has the correct dimension of time.
 ## OPTION ANALYSIS
[A] :x: Incorrect, this is the square of g
[B] :x: Incorrect, this is the value of g
[C] :x: Incorrect, this is the square root of g
[D] ✓: Correct, this is the reciprocal of the square root of g
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing kg wt with kg. Remember kg wt is a unit of force, while kg is a unit of mass.
		2.[Error 2]: Incorrectly applying the formula for force.
	**Quick Tips**:
		1.[Helpful shortcut]: Remember that force has units of mass * length / time², and use dimensional analysis to derive the time unit.
		2.[Memory aid]: Keep in mind that weight is a force due to gravity (F = mg), and g has units of m/s².

ABDUL JILANI BASHA · Answer

${\left( {9.8} \right)^2}\,\sec $

ABDUL JILANI BASHA · Answer

9.8 sec

ABDUL JILANI BASHA · Answer

$\sqrt {9.8} \,\sec $

ABDUL JILANI BASHA · Answer

The correct Option is "$\frac{1}{{\sqrt {9.8} }}\,\sec $"

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