Question

If the unit of force is 1KN, the length is 1Km and time is 100s what will be the unit of mass?
A. 1000 Kg
B. 1Kg
C. 10000Kg
D. 100Kg

Answer 1

Hint: Force is defined as acceleration given to a body of mass to get the motion. Acceleration is defined as velocity per unit time while velocity is nothing but displacement per unit time. So use the formula of force, acceleration as well as velocity. Notice option given in the question is in kilogram not in gram.

Complete step by step solution:
Aim: Find the unit of mass.
We know that, in simple words, force is nothing but the product of mass and acceleration. $force=mass\times acceleration$
Mathematically force is given by,
$F=m\times a$
Where,
F= unit of force
m= unit of mass
a= acceleration
But we know that,
Acceleration is defined as velocity per unit time.
Mathematically,
$a=\dfrac{v}{t}$
Where,
 v= unit of velocity
t= time in second
Again, we know that velocity is defined as distance cover in meter by time.
$v=\dfrac{d}{t}$
Where,
d= distance or length covered
t= time in second
So finally formula of velocity can be written as,
$F=m\times \dfrac{d}{{{t}^{2}}}$
Given data:
F= 1KN (unit of force)
d= 1Km (length)
t= 100s (time)
Put all the value in the formula of force (F),
${{10}^{-3}}=m\times \dfrac{{{10}^{-3}}}{{{(1000)}^{2}}}$
${{10}^{-3}}\times {{10}^{6}}=m{{10}^{-3}}$
\[m=\dfrac{{{10}^{-3}}\times {{10}^{6}}}{{{10}^{-3}}}\]
Cancel like terms from denominator and numerator,
$m={{10}^{6}}g$
Now our answer is in gram (g), but options are given in kilogram. So convert gram into kilogram (Kg)
We get,
$m={{10}^{3}}Kg=1000Kg$
So the unit of mass is $(m)=1000Kg$
Answer- (A)

Note: Here you may get confused between velocity and speed in force formula. In this case, you can consider either speed or velocity. Difference between velocity and speed is, velocity is nothing but displacement by the time that is the distance between two points and it is a vector quantity. While speed is nothing but the total distance covered per unit time and it is a scalar quantity.
We know that, 1Kg = 1000gram(g) or 1000Kg = 10,00,000gram(g).