16. The velocity v of a particle at time t is given by v = at +	b	, where a, b and c are constant.
    	t + c

    The dimensions of a, b and c are respectively​​
    

1. 1. ​L², T and LT² ​

   
   
   

   2. LT², LT and L

   
   
   

   3. L, LT and T² ​

   
   
   

   4. ​LT^{– 2}, L and T

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Dimension of  a. t = dimension of velocity​ ​
   a .t = L T^-1 ⇒ a = LT^-2
   Dimension of c = dimension of t
   ​(two physical quantity of same dimension can only be added)
   So, dimension of c = T
   

   Dimension of	b	= Dimension of v
   	t + c

   
   

   	b	= L T-1 ⇒ b.T-1 = LT-1 ⇒ b = L
   	T + T

   
   So, answer is LT^-2, L & T
   

   Correct Option: D

   Dimension of  a. t = dimension of velocity​ ​
   a .t = L T^-1 ⇒ a = LT^-2
   Dimension of c = dimension of t
   ​(two physical quantity of same dimension can only be added)
   So, dimension of c = T
   

   Dimension of	b	= Dimension of v
   	t + c

   
   

   	b	= L T-1 ⇒ b.T-1 = LT-1 ⇒ b = L
   	T + T

   
   So, answer is LT^-2, L & T
   

---

17. The ratio of the dimension of Planck’s constant and that of the moment of inertia is the dimension of​​​
    

1. 1. time

   
   
   

   2. frequency

   
   
   

   3. angular momentum

   
   
   

   4. velocity

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Plank 's constant	=	2πIω
   Moment of inertia		n
   		I

   
   

   [ As	nh	= Iω ]
   	2π

   
   

   2πI(2πf)	=		4π2 f		= [T-1]
   nI			n

   Correct Option: B

   Plank 's constant	=	2πIω
   Moment of inertia		n
   		I

   
   

   [ As	nh	= Iω ]
   	2π

   
   

   2πI(2πf)	=		4π2 f		= [T-1]
   nI			n

---

---

18. The dimensions of universal gravitational constant are​​​
    

1. 1. M^{– 2} L² T^{– 1} ​

   
   
   

   2. M^{– 1}  L³ T^{– 2}

   
   
   

   3. M L² T^{– 1}

   
   
   

   4. ​M^{– 2} L³ T^{– 2}

   
   
   

---

1. View Hint View Answer Discuss in Forum

   F =	G M1m1	⇒ G =	F r2
   	r2		M1m1

   
   

   ∴ dimension of G is	MLT-2 [L2]	= M-1L3T-2
   	[M] [M]

   Correct Option: B

   F =	G M1m1	⇒ G =	F r2
   	r2		M1m1

   
   

   ∴ dimension of G is	MLT-2 [L2]	= M-1L3T-2
   	[M] [M]

---

19. The dimensions of Planck’s constant are same as ​​
    

1. 1. energy

   
   
   

   2. power

   
   
   

   3. momentum

   
   
   

   4. ​angular momentum

   
   
   

---

1. View Hint View Answer Discuss in Forum

   We know that E = hυ
   

   h =	E	=	[ML2T-2]	= [ML2T-1]
   	υ		[T-1]

   
   Angular momentum = Iω ​
   = [ML²][T ^{– 1}] = [ML²T ^{– 1}]

   Correct Option: D

   We know that E = hυ
   

   h =	E	=	[ML2T-2]	= [ML2T-1]
   	υ		[T-1]

   
   Angular momentum = Iω ​
   = [ML²][T ^{– 1}] = [ML²T ^{– 1}]

---

---

20. Which one of the following groups have quantities that do not have the same dimensions?​​
    

1. 1. pressure, stress

   
   
   

   2. velocity, speed ​

   
   
   

   3. force, impulse

   
   
   

   4. work, energy

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Force has dimension [MLT ^{– 2}] while impulse has dimension [MLT ^{– 1}], both have different dimensions.

   Correct Option: C

   Force has dimension [MLT ^{– 2}] while impulse has dimension [MLT ^{– 1}], both have different dimensions.

---