Question

If the present units of length, time and mass (m, s, kg) are changed to 100m, 100s and $\dfrac{1}{{10}}kg$, then how will the new unit of force change?

Answer 1

Hint: The unit of force must be written in terms of the basic units of length, mass and time. Then, the new units must be substituted to calculate the new unit of force with this change.

Complete step by step answer:
The definition of force is given by the Newton’s second law of motion, which states that “force is directly proportional to the rate of change of momentum”
Mathematically, the force is given by –
$F = ma$
Where m=mass of the body, a=acceleration,
Therefore, the unit of force = Newton (N) = $kg \times m{s^{ - 2}}$
Let the new unit of force = ${N_1} = k{g_1} \times {m_1}s_1^{ - 2}$

Now from the given data of new units we have,
$k{g_1} = \dfrac{{kg}}{{10}}$
${m_1} = 100m$
${s_1} = 100s$

Now substitute all the values of new units in new equation of force and simplifying we get,
${N_1} = k{g_1} \times {m_1}s_1^{ - 2}$
${N_1} = \dfrac{{kg}}{{10}} \times 100m \times {100^{ - 2}}s$
${N_1} = \dfrac{1}{{10}} \times 100 \times {100^{ - 2}}kg - m{s^{ - 2}}$
$ \Rightarrow {N_1} = {10^{ - 3}}N$
Hence, The new unit of force is equal to ${N_1} = {10^{ - 3}}N$

Note: The unit of force, newton belongs to the SI system. In the CGS system, there is another unit of force, known as the dyne. Their relationship is given as –
$1N = {10^5}dyne$