Question

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

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

Answer 1

Answer: (A)

1/10 N

Answer 2

n₁u₁ = n₁u₂

Let 1 dyne = nu

Where u = new unit of force[F] = [M¹L¹T^–2]

1 gm. cm.s^–2 = n.(10gm) . (10cm) . (0.1s)^–2

where 10 gm, 10 cm are 0.1 s are new units of mass, length and time respectively

solving the above relation we get n = 10^–4

i.e. 1 dyne = 10^–4u

or 10^–5 newton = 10^–4 u

or $u = \frac{1}{10}$ Newton