11. The dimensions of ( μ₀ ∊₀ ) ^{– 1 / 2} are
    

1. 1. [L^{1 / 2} T ^{– 1 / 2}]

   
   
   

   2. ​[L ^{– 1} T]

   
   
   

   3. [L T ^{– 1}]

   
   
   

   4. ​[L ^{– 1 / 2} T ^{1 / 2}]

   
   
   

---

1. View Hint View Answer Discuss in Forum

   (μ0ε0)-1 / 2 =	1	= c : speed of light
   	√μ0ε0

   
   where ε₀ =  permittivity of free space
   μ₀ = permeability of free space ​
   So dimensions are  [LT ^{– 1}]

   Correct Option: C

   (μ0ε0)-1 / 2 =	1	= c : speed of light
   	√μ0ε0

   
   where ε₀ =  permittivity of free space
   μ₀ = permeability of free space ​
   So dimensions are  [LT ^{– 1}]

---

12. The unit of permittivity of free space, εo is
    

1. 1. Coulomb²/(Newton-metre)²

   
   
   

   2. Coulomb/Newton-metre

   
   
   

   3. Newton-meter²/Coulomb² ​

   
   
   

   4. Coulomb²/Newton-meter²

   
   
   

---

1. View Hint View Answer Discuss in Forum

   ε0 =	q2
   	(r2) 4 π F

   
   ⇒ unit of εo is (coulomb)² / newton-metre²

   Correct Option: D

   ε0 =	q2
   	(r2) 4 π F

   
   ⇒ unit of εo is (coulomb)² / newton-metre²

---

---

13. ​In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to
    

1. 1. 0.1 N

   
   
   

   2. 1 N

   
   
   

   3. 10 N

   
   
   

   4. ​100 N

   
   
   

---

1. View Hint View Answer Discuss in Forum

   [F] = MLT ^{– 2} = (10g) (10 cm) (0.1s) ^{– 2}
   ​= (10 ^{– 2} kg) (10 ^{– 1}m) (10 ^{– 1}s) ^{– 2} = 10 ^{– 1} N.
   

   Correct Option: A

   [F] = MLT ^{– 2} = (10g) (10 cm) (0.1s) ^{– 2}
   ​= (10 ^{– 2} kg) (10 ^{– 1}m) (10 ^{– 1}s) ^{– 2} = 10 ^{– 1} N.
   

---

14. The unit of the Stefan-Boltzmann's constant is​​​
    

1. 1. W/m²K⁴

   
   
   

   2. W/m²

   
   
   

   3. W/m²K

   
   
   

   4. W/m²K²

   
   
   

---

1. View Hint View Answer Discuss in Forum

   ​E = σAT⁴ ​
   E is energy dissipated per second.
   

   σ =	E	=	Watt
   	AT4		m2 K4

   Correct Option: A

   ​E = σAT⁴ ​
   E is energy dissipated per second.
   

   σ =	E	=	Watt
   	AT4		m2 K4

---

---

15. If x = at + bt², where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is​​
    

1. 1. ​km/s

   
   
   

   2. kms

   
   
   

   3. km/s²

   
   
   

   4. ​kms²

   
   
   

---

1. View Hint View Answer Discuss in Forum

   [x] = [bt²].
   Hence [b] = [x / t²] = km/s².

   Correct Option: C

   [x] = [bt²].
   Hence [b] = [x / t²] = km/s².

---