Question

if the units of force,energy and velocity are 200 dyne,1000erg and 10 cms^-2 respectively.Find. the units of length,mass and time.

Answer 1

Since, Units of force,energy and velocity are 200 dyne,1000 erg and 10 cms⁻¹, then,

[MLT⁻²] = 200 dyne     ..............eq(i)

[ML²T⁻²] = 1000 erg or 1000 dyne cm.      ............eq(ii)

[LT⁻¹] = 10 cms⁻¹    ...........eq(iii)

Dividing eq(i) from eq(ii), we will get,

L = 5 cm.

Putting it in eq(iii),

T⁻¹ = 2 s⁻¹

T = 2 seconds.

Similarly,

[M] × 5 cm × (2 s)⁻² = 200 gcms⁻²

[M] = (200/5) × 4 gcms⁻²/cms⁻²

⇒ [M] = 160 g.

Hope it helps.