The pair of quantities having same dimensions is
(a) Young’s modulus and energy (b) impulse and surface tension (c) angular momentum and work (d) work and torque
Answers
option (d) work and torque
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The pair of quantities having the same dimensions is ..
- (a) Young's modulus and energy
- (b) impulse and surface tension
- (c) angular momentum and work
- (d) work and torque
(a) Young's modulus and energy
Young's modulus is the ratio of stress to strain. dimensions of stress is as same as that of pressure. but strain is dimensionless. hence, the dimensions of Young's modulus is dimensions of pressure.
∴ dimensions of Young's modulus ≠ dimensions of energy
(b) Impulse and surface tension
impulse is the change in linear momentum of a system. so the dimension of impulse is kgm/s.
surface tension is proportional to ratio of force to length. hence the dimensions of surface tension = dimensions of force/dimensions of length
= (kgm/s²)/m = kg/s²
∴ dimensions of impulse ≠ dimensions of surface tension
(c) angular momentum and work
Angular momentum = mass × velocity × distance
dimensions of angular momentum = kg × m/s × m = kgm²/s
But work = force × displacement
dimensions of work = kgm/s² × m = kgm²/s²
∴ dimensions of angular momentum ≠ dimensions of work
(d) work and torque
work = force × displacement
dimensions of work = kgm/s² × m = kgm²/s²
And torque = force × displacement
dimensions of torque = kgm²/s²
∴ dimensions of work ≠ dimensions of torque
Therefore the correct option (d) work and torque.
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