Question

30 If the unit of force is 1 kilonewton, the length is 1 km
and time is 100 second, what will be the unit of mass :
(1) 1000 kg
(2) 10 kg
(3) 10000 kg
(4) 100 kg
E1-5​

Answer 1

Given :

• Force (F) = 1kN = 1000 N
• Distance (x) = 1 km = 1000 m
• Time (t) = 100 s

To Find :

• Unit of Mass

Solution :

As, we know :

$\implies \sf{F \: = \: [MLT^{-2}]}$

And,

$\implies \sf{F \: = \: \dfrac{Mass \: \times \: Distance}{Time^2}} \\ \\ \implies \sf{Mass \: = \: \dfrac{Force \: \times \: Time^2}{Distance}} \\ \\ \implies \sf{Mass \: = \: \dfrac{1000 \: \times \: 100^2}{1000}} \\ \\ \implies \sf{Mass \: = \: \dfrac{1000 \: \times \: 100 \: \times \: 100}{1000}} \\ \\ \implies \sf{Mass \: = \: \dfrac{10000000}{1000}} \\ \\ \implies \sf{Mass \: = \: 10000}$

$\therefore$ Unit of mass is 10000 kg

Answer 2

$\rule{300}3$

$\leadsto$Force = $\rm M^1 L^1 T^-^2$

$\leadsto$1000 N = (kg) × (1000)mt/(100)²s²

$\leadsto$Mass (kg) = 1000 × (100)²/ 1000

$\leadsto$10000 kg

$\rule{300}3$