Question

In a particular system, the unit of length, mass and time are chosen to be 10cm, 10gm and 0.1s respectively. The unit of force in this system will be equivalent to –

• A. 1/10 N
• B. 1N
• C. 10N
• D. 100N

Answer 1

Answer: (A)

1/10 N

Answer 2

Dimensionally

$\text{F }\mathbf{=}\text{ ML}\text{T}^{\text{-2}}$ In C.G.S. system

1 dyne = 1g 1cm (1s)^–2

In new system

1x = (10g) (10cm) (0.1s)^–2

$\frac{1dyne}{1x}$ = $\frac{1g}{10g}$ × $\frac { 1 \mathrm {~cm} } { 10 \mathrm {~cm} }$ $\left( \frac{10s}{1s} \right)^{- 2}$

1 dyne = $\frac{1}{10,000}$×1x

$\text{1}\text{0}^{4}\text{ dyne } = \text{ 1x}$

$\text{10x } = \text{ 1}\text{0}^{5}\text{ dyne } = \text{ 1N}$

x = $\frac{1}{10}$N.