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Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then - 
  • a)
    α + p = 2 β
  • b)
    p + q – r = β 
  • c)
    p − q + r = α
  • d)
    p + q + r = β
Correct answer is option 'A,B'. Can you explain this answer?
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Sometimes it is convenient to construct a system of units so that all ...
], [time] = [X], [mass] = [X]^3, [force] = [X]^2.

This system of units is known as the natural system of units or Planck units. It is based on fundamental physical constants such as the speed of light, Planck's constant, and the gravitational constant. In this system, the quantity X is chosen to be the Planck length, which is the length scale at which quantum effects become significant in the context of gravity.

Using the natural system of units can simplify calculations in theoretical physics and cosmology where the Planck length and other fundamental constants play a significant role. However, in practical applications, it is more common to use other systems of units such as the SI system or the CGS system.
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Sometimes it is convenient to construct a system of units so that all ...
Given L = xα ……(1)
LT–1 = xβ ……(2)
LT–2 = xp ……(3)  
MLT–1 = xq ……(4)  
MLT–2 = xr ……(5)

From (3) 

From (4)  
M = xq–β
From (5)  ⇒ xq = xr  xα-β
⇒ α + r – q = β ……(6)
Replacing value 'α' in equation (6) from (A) 
2β – p + r – q = β
⇒ p + q – r = β (B) 
Replacing value of 'β' in equation (6) from (A) 
2α + 2r – 2q = α + p 
α = p + 2q – 2r
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Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -a)α + p = 2 βb)p + q – r = βc)p − q + r = αd)p + q + r =βCorrect answer is option 'A,B'. Can you explain this answer?
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Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -a)α + p = 2 βb)p + q – r = βc)p − q + r = αd)p + q + r =βCorrect answer is option 'A,B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -a)α + p = 2 βb)p + q – r = βc)p − q + r = αd)p + q + r =βCorrect answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -a)α + p = 2 βb)p + q – r = βc)p − q + r = αd)p + q + r =βCorrect answer is option 'A,B'. Can you explain this answer?.
Solutions for Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [Xα]; [speed] = [Xβ]; [acceleration] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -a)α + p = 2 βb)p + q – r = βc)p − q + r = αd)p + q + r =βCorrect answer is option 'A,B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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