26. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively.

    Quantity P is calculated as follows P =	a3 b2	% error in P is :
    	cd

    
    

1. 1. 10%

   
   
   

   2. 7%

   
   
   

   3. 4%

   
   
   

   4. 14%

   
   
   

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1. View Hint View Answer Discuss in Forum

   P =

   a3 b2

   ,

   ∆P

   × 100% = 3

   ∆a

   × 100% + 2

   ∆b

   × 100% +

   ∆c

   × 100% +

   ∆d

   × 100%

   cd

   P

   a

   b

   c

   d

   
   = 3 × 1% + 2 × 2% + 3% + 4% = 14%

   Correct Option: D

   P =

   a3 b2

   ,

   ∆P

   × 100% = 3

   ∆a

   × 100% + 2

   ∆b

   × 100% +

   ∆c

   × 100% +

   ∆d

   × 100%

   cd

   P

   a

   b

   c

   d

   
   = 3 × 1% + 2 × 2% + 3% + 4% = 14%

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27. If C and R denote capacitance and resistance, the dimensional formula of CR is​
    

1. 1. [M⁰L⁰T¹] ​

   
   
   

   2. [M⁰L⁰T⁰]

   
   
   

   3. [M⁰L⁰T^{– 1}]

   
   
   

   4. not expressible in terms of M,L,T.

   
   
   

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1. View Hint View Answer Discuss in Forum

   CR = [M^–1L^–2T⁴A²] [M¹L²T^–3A^–2]
   = [M⁰L⁰T¹] ​
   

   Correct Option: A

   CR = [M^–1L^–2T⁴A²] [M¹L²T^–3A^–2]
   = [M⁰L⁰T¹] ​
   

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28. The dimensional formula for angular momentum is​​
    

1. 1. ​[M⁰L²T ^–2] ​

   
   
   

   2. [ML²T ^–1] ​

   
   
   

   3. ​[MLT ^–1] ​

   
   
   

   4. [ML²T ^–2]

   
   
   

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1. View Hint View Answer Discuss in Forum

   [Angular momentum ] ​= [Momentum of inertia] × [Angular velocity] ​
   = ML² × T^–1 ​= ML²T^–1

   Correct Option: B

   [Angular momentum ] ​= [Momentum of inertia] × [Angular velocity] ​
   = ML² × T^–1 ​= ML²T^–1

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29. Of the following quantities, which one has dimension different from the remaining three? ​
    

1. 1. Energy per unit volume ​

   
   
   

   2. Force per unit area ​

   
   
   

   3. Product of voltage and charge per unit volume

   
   
   

   4. Angular momentum.

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​For angular momentum, the dimensional formula is ML²T^–1. For other three, it is ML ^–1T^–2.

   Correct Option: D

   ​For angular momentum, the dimensional formula is ML²T^–1. For other three, it is ML ^–1T^–2.

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30. Dimensional formula of self inductance is​​​
    

1. 1. ​[MLT ^–2A ^–2]

   
   
   

   2. [ML²T ^–1A ^–2]

   
   
   

   3. ​[ML²T ^–2A ^–2] ​

   
   
   

   4. ​[ML²T ^–2A ^–1]

   
   
   

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1. View Hint View Answer Discuss in Forum

   L = ε

   dt

   =

   W

   T

   dI

   q

   t

   
   

   or , [L] =	[ML2T–2] [T]	= ML2T–2A–2
   	[AT] [A]

   
   

   Correct Option: C

   L = ε

   dt

   =

   W

   T

   dI

   q

   t

   
   

   or , [L] =	[ML2T–2] [T]	= ML2T–2A–2
   	[AT] [A]

   
   

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