41. An equation is given as :		p +	a		- b	θ
    			V2			V

    
    where P = Pressure, V = Volume & θ = Absolute temperature. If a and b are constants, then dimensions of a will be

1. 1. [ML⁵T^{– 2}]

   
   
   

   2. [M^–1L⁵T²] ​

   
   
   

   3. ​[ML^{– 5}T^{– 1}]

   
   
   

   4. [ML⁵T¹]

   
   
   

---

1. View Hint View Answer Discuss in Forum

   		p +	a		= b	Q
   			V2			V

   
   According to the principle of homogeinity quantity with same dimension can be added or subtracted. ​
   

   Hence, Dimension of P = Dimension of	a
   	V2

   
   

   ⇒ Dimension of	Force	= Dimension of	a
   	Area		V2

   
   

   ⇒			MLT-2			=	a	⇒ a = [M L5 T-2]
   			L2				[L3]2

   
   

   Correct Option: A

   		p +	a		= b	Q
   			V2			V

   
   According to the principle of homogeinity quantity with same dimension can be added or subtracted. ​
   

   Hence, Dimension of P = Dimension of	a
   	V2

   
   

   ⇒ Dimension of	Force	= Dimension of	a
   	Area		V2

   
   

   ⇒			MLT-2			=	a	⇒ a = [M L5 T-2]
   			L2				[L3]2

   
   

---

42. The force F on a sphere of radius  a moving in a medium with velocity v is  given by F = 6πηav. The dimensions of η are ​​

1. 1. [ML^{– 3}]

   
   
   

   2. ​[ML^{– 2}] ​

   
   
   

   3. ​[ML^{– 1}]

   
   
   

   4. [ML^{– 1}T^{– 1}]
      

   
   
   

---

1. View Hint View Answer Discuss in Forum

   F = 6πη av
   

   η =	F	=	[MLT-2]	= [ML-1T-1]
   	6π av		[L] [LT-1]

   Correct Option: D

   F = 6πη av
   

   η =	F	=	[MLT-2]	= [ML-1T-1]
   	6π av		[L] [LT-1]

---

---