Question

Match column 1 with column 2.

Column 1	Column 2
i) 1 Newton	p) 9.8N
ii) 1 dyne	q)980 dyne
iii) 1kgf	r) $1kgm{{s}^{-2}}$
iv) 1gf	s) $1gcm{{s}^{-2}}$

Answer 1

The above question is of the form match the following with correct answers. If we observe the above two columns they basically contain, some physical units. More precisely, they are related to each other as equivalent units which are expressed in MKS and CGS systems of units. Hence we will first understand how they are equivalent to each other and accordingly match the following.

Complete step-by-step answer:
To begin with let us first understand what does 1 Newton mean. The SI unit of force is defined as Newton(N). If the magnitude of the force is one then we say that the force of 1 Newton acts on the body. The unit N of magnitude 1, can be written in terms of fundamental physical dimension which is equal to $1kgm{{s}^{-2}}$. Hence the correct answer of the first one is option r in column 2.
Dyne refers to the force expressed in the CGS system i.e. the mass is expressed in terms of gram(g), the distance is expressed in terms of centimeter(cm) and time in terms of seconds(s). One dyne refers to the magnitude of the force is 1 unit respectively. The unit dyne of magnitude 1can be written in terms of fundamental physical dimension which is equal to $1gcm{{s}^{-2}}$. Hence the correct answer of the second is option s from column 2.
Kgf is the unit used to represent the gravitation weight. 1kgf refers to the weight of the body or the force of gravity with mass 1 kilogram. Since gravitational force is defined as mass times acceleration due to gravity i.e. $g=9.8m{{s}^{-2}}$, the force on the body is equal to,
$\begin{aligned} & F=mg=1kg\times 9.8m{{s}^{-2}} \\\ & \Rightarrow F=9.8kgm{{s}^{-2}} \\\ & \Rightarrow F=9.8N \\\ \end{aligned}$
Therefore the correct answer of the third one is option p.
We know that,
$\begin{aligned} & 1kgf=9.8kgm{{s}^{-2}} \\\ & \Rightarrow 1gf=\dfrac{9.8}{{{10}^{3}}}kgm{{s}^{-2}}\text{, }1cm={{10}^{-2}}m \\\ & \Rightarrow 1gf=9.8\times {{10}^{3}}\times {{10}^{-1}}g\times {{10}^{-2}}m{{s}^{-2}} \\\ & \Rightarrow 1gf=9.8\times {{10}^{2}}gcm{{s}^{-2}} \\\ & \Rightarrow 1gf=980gcm{{s}^{-2}}\text{, }\because gcm{{s}^{-2}}=dyne \\\ & \Rightarrow 1gf=980dyne \\\ \end{aligned}$
Hence the correct answer of the fourth one is option q in column 2.

Note: It is to be noted that the conversion of units can be done easily when we know what does the unit mean and the power of the unit with respect to the SI unit. For the fourth option we could have cancelled the kilo multiplier and directly concluded to some other result. But always remember that whenever a weight is expressed in terms of grams always see if you can convert it to CGS.