31. The dimensional formula of torque is
    

1. 1. ​[ML²T^-2]

   
   
   

   2. ​[MLT ^–2] ​

   
   
   

   3. ​[ML ^–1T ^–2]

   
   
   

   4. ​[ML ^–2T ^–2]

   
   
   

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1. View Hint View Answer Discuss in Forum

   τ = [Force × distance]
   = [MLT^–2] [L] = ML²T^–2

   Correct Option: A

   τ = [Force × distance]
   = [MLT^–2] [L] = ML²T^–2

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32. The dimensional formula of pressure is
    

1. 1. [MLT ^–2] ​

   
   
   

   2. [ML ^–1T²] ​

   
   
   

   3. [ML ^–1T ^–2]

   
   
   

   4. [MLT²]

   
   
   

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1. View Hint View Answer Discuss in Forum

   [Pressure] = [Force] / [Area]
   

   =	[MLT–2]	= ML–1T–2
   	L2

   Correct Option: C

   [Pressure] = [Force] / [Area]
   

   =	[MLT–2]	= ML–1T–2
   	L2

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33. A certain body weighs 22.42 gm and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 gm and 0.1 cc. Then maximum error in the density will be
    

1. 1. 22%

   
   
   

   2. 2%​

   
   
   

   3. 0.2%

   
   
   

   4. 0.02%

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​Density, D = M/V
   

   ∴

   ∆D

   =

   ∆M

   +

   ∆V

   =

   0.01

   +

   0.01

   × 100 = 2%

   D

   M

   V

   22.42

   4.7

   Correct Option: B

   ​Density, D = M/V
   

   ∴

   ∆D

   =

   ∆M

   +

   ∆V

   =

   0.01

   +

   0.01

   × 100 = 2%

   D

   M

   V

   22.42

   4.7

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34. According to Newton, the viscous force acting between liquid layers of area A and velocity gradient

    ∆V/∆Z is given by F = -η A	∆V	where η is constant called coefficient of viscosity.
    	∆Z

    The dimensional formula of η is​​
    

1. 1. ML ^{– 2}T ^–2​

   
   
   

   2. M⁰​L⁰​T⁰​

   
   
   

   3. ML²​T ^–2​

   
   
   

   4. ML ^–1​T ^–1​

   
   
   

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1. View Hint View Answer Discuss in Forum

   Substitute the dimensional formula of F, A, ∆V and ∆Z on both sides and find that for η.

   Correct Option: D

   Substitute the dimensional formula of F, A, ∆V and ∆Z on both sides and find that for η.

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35. The dimensional formula for permeability µ is given by​​

1. 1. MLT ^{– 2}A ^{– 2}

   
   
   

   2. M⁰L¹T ​

   
   
   

   3. M⁰L²T ^{– 1}A² ​

   
   
   

   4. None of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   μ =	B	; [B] = MT– 2 A– 1
   	nI

   
   [n] = L^{– 1} , [I] = A
   

   	B		= [MLT– 2A– 2]
   	nI

   
   

   Correct Option: A

   μ =	B	; [B] = MT– 2 A– 1
   	nI

   
   [n] = L^{– 1} , [I] = A
   

   	B		= [MLT– 2A– 2]
   	nI

   
   

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