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The pair having the same dimensions is
- a)Angular momentum, work
- b)Work, torque
- c)Potential energy, linear momentum
- d)Kinetic energy, velocity
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The pair having the same dimensions isa)Angular momentum, workb)Work, ...
Explanation:
Two physical quantities are said to have the same dimensions if both the physical quantities have the same fundamental dimensions. The fundamental dimensions are mass, length and time.
Dimensions of Work and Torque:
The dimension of work is [M L^2 T^-2] and the dimension of torque is [M L^2 T^-2]. Both have the same dimensions, hence option B is the correct answer.
Other options:
a) Angular momentum has dimension [M L^2 T^-1]. It doesn't have the same dimensions as work.
c) Potential energy has dimension [M L^2 T^-2]. Linear momentum has dimension [M L T^-1]. They don't have the same dimensions.
d) Kinetic energy has dimension [M L^2 T^-2]. Velocity has dimension [L T^-1]. They don't have the same dimensions.
Two physical quantities are said to have the same dimensions if both the physical quantities have the same fundamental dimensions. The fundamental dimensions are mass, length and time.
Dimensions of Work and Torque:
The dimension of work is [M L^2 T^-2] and the dimension of torque is [M L^2 T^-2]. Both have the same dimensions, hence option B is the correct answer.
Other options:
a) Angular momentum has dimension [M L^2 T^-1]. It doesn't have the same dimensions as work.
c) Potential energy has dimension [M L^2 T^-2]. Linear momentum has dimension [M L T^-1]. They don't have the same dimensions.
d) Kinetic energy has dimension [M L^2 T^-2]. Velocity has dimension [L T^-1]. They don't have the same dimensions.
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Community Answer
The pair having the same dimensions isa)Angular momentum, workb)Work, ...
Torque is vector whereas work is a scalar..they are not equal by direction but magnitudinally both are same...so, dimensions are also equal.
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The pair having the same dimensions isa)Angular momentum, workb)Work, torquec)Potential energy, linear momentumd)Kinetic energy, velocityCorrect answer is option 'B'. Can you explain this answer?
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