36. P represents radiation pressure, c represents speed of light and S represents radiation energy striking unit area per sec. The non zero integers x, y, z such that P^x S^y c^z is dimensionless are​​
    

1. 1. x = 1, y = 1, z = 1 ​

   
   
   

   2. x = – 1, y = 1, z = 1 ​

   
   
   

   3. x = 1, y = – 1, z = 1​ ​

   
   
   

   4. ​x = 1, y = 1, z = – 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Try out the given alternatives. ​
   When x = 1, y =  – 1, z = 1 ​
   

   Px Sy cz = P1 S-1 c1 =	Pc
   	S

   
   

   =	[M L – 1 T-2 [LT – 1]	= M0L0T0
   	[M L 2 T– 2 / L2 T]

   Correct Option: C

   Try out the given alternatives. ​
   When x = 1, y =  – 1, z = 1 ​
   

   Px Sy cz = P1 S-1 c1 =	Pc
   	S

   
   

   =	[M L – 1 T-2 [LT – 1]	= M0L0T0
   	[M L 2 T– 2 / L2 T]

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37. Turpentine oil is flowing through a tube of length L and radius r. ​The pressure difference between the two ends of the tube is p. The viscosity of oil is given by
    

    η =	p(r2 - x2)
    	4vl

    
    where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of η are ​
    

1. 1. [M⁰L⁰T⁰] ​

   
   
   

   2. [MLT ^{– 1}] ​

   
   
   

   3. [ML²T ^{– 2}]

   
   
   

   4. [ML ^{– 1}T ^{– 1}]

   
   
   

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1. View Hint View Answer Discuss in Forum

   h =	p(r2 - x2)	=	[ML – 1T-2] [L2]	= [ML – 1T – 1]
   	4vl		[LT – 1] [L]

   Correct Option: D

   h =	p(r2 - x2)	=	[ML – 1T-2] [L2]	= [ML – 1T – 1]
   	4vl		[LT – 1] [L]

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38. The time dependence of a physical quantity p is given by p = p₀ exp ( – α t²), where α is a constant and t is the time. The constant α  ​
    

1. 1. ​is dimensionless

   
   
   

   2. has dimensions T^{– 2}​

   
   
   

   3. has dimensions T² ​

   
   
   

   4. ​has dimensions of p

   
   
   

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1. View Hint View Answer Discuss in Forum

   In p = p₀ exp ( – αt²), αt² dimensionless
   

   ∴ α -	I	-	I	- [T-2]
   	t2		T2

   
   

   Correct Option: B

   In p = p₀ exp ( – αt²), αt² dimensionless
   

   ∴ α -	I	-	I	- [T-2]
   	t2		T2

   
   

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39. Which of the following is a dimensional constant?
    

1. 1. Refractive index ​

   
   
   

   2. Poissons ratio ​

   
   
   

   3. Relative density ​

   
   
   

   4. Gravitational constant

   
   
   

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1. View Hint View Answer Discuss in Forum

   A quantity which has dimensions and a constant value is called dimensional constant. Therefore, gravitational gravitational constant (G) is a dimensional constant.

   Correct Option: D

   A quantity which has dimensions and a constant value is called dimensional constant. Therefore, gravitational gravitational constant (G) is a dimensional constant.

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40. Which of the following will have the dimensions of time​​​
    

1. 1. LC

   
   
   

   2. 	R
      	L

   
   
   

   3. 	L
      	R

   
   
   

   4. 	C
      	L

   
   
   

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1. View Hint View Answer Discuss in Forum

   e = - L	di	.........(1)
   	dt

   
   e = iR​​.........(2)
   

   From (1) & (2) , iR = - L	di
   	dt

   
   ∴​ Dimension of L.H.S. = Dimension of R.H.S. ​
   

   [A] R = L [AT – 1] ⇒	L	= [T]
   	R

   Correct Option: C

   e = - L	di	.........(1)
   	dt

   
   e = iR​​.........(2)
   

   From (1) & (2) , iR = - L	di
   	dt

   
   ∴​ Dimension of L.H.S. = Dimension of R.H.S. ​
   

   [A] R = L [AT – 1] ⇒	L	= [T]
   	R

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