6. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be​

1. 1. ML²T ^{– 2}

   
   
   

   2. ML²T ^{– 1}I ^{– 1}

   
   
   

   3. ML²T ^{– 3}I ^{– 2}

   
   
   

   4. ML²T ^{– 3}I ^{– 1}

   
   
   

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   Dimensions of Resistance, =	[V]	=	[ML2T-3I-1]	= [ML2T-3I-2]
   	[I]		[I]

   Correct Option: C

   Dimensions of Resistance, =	[V]	=	[ML2T-3I-1]	= [ML2T-3I-2]
   	[I]		[I]

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7. 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}

   
   
   

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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]

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8. 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

   
   
   

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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.

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

1. 1. energy

   
   
   

   2. power

   
   
   

   3. momentum

   
   
   

   4. ​angular momentum

   
   
   

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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}]

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10. The pair of quantities having same dimensions is​​
    

1. 1. Young’s modulus and energy

   
   
   

   2. impulse and surface tension ​

   
   
   

   3. angular momentum and work

   
   
   

   4. work and torque

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work = Force ×  displacement ​
   Torque = Force × force arm ​ 
   = mass × acceleration × length ​ 
   = [M] × [LT ^{– 2}] × [L] = [M L²T ^{– 2}]

   Correct Option: D

   Work = Force ×  displacement ​
   Torque = Force × force arm ​ 
   = mass × acceleration × length ​ 
   = [M] × [LT ^{– 2}] × [L] = [M L²T ^{– 2}]

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