Question

If the unit of power is 100 erg/minute, the unit of force is 100 dyne and the unit of time is 100 seconds, the unit of length is (in cm)

Answer 1

Given : The unit of power is 100 erg/minute, the unit of force is 100 dyne and the unit of time is 100 seconds.

To find : the unit of length.

solution : we know, energy = power × time i.e., E = P × t

also energy = work done = Force × displacement i.e., E = F × s

so, E = P × t = F × s

⇒P × t = F × s

here unit of power = P = 100 erg/min = 100 dyne cm/60 sec = 5/3 Dyne cm/ sec

unit of force = F = 100 dyne

unit of time = 100 sec

now, 5/3 Dyne cm/sec × 100 sec = 100 Dyne × s

⇒s = 5/3 cm

Therefore unit of length is 5/3 cm