Question

Weight of 1kg mass on earth is equal to:
A) $9 \cdot 8 \times {10^5}dynes$.
B) $9 \cdot 8dynes$.
C) $98dynes$.
D) None of these.

Answer 1

The force is defined as the pull or push on any object. Mathematically it is defined as the product of mass and acceleration. The force is directly proportional to the mass of the object and the acceleration of the object.

Formula used:
The formula of the weight is given by,
$\Rightarrow F = m \times g$
Where force is F the mass of the object is m and the acceleration due to gravity is g.

Complete step by step solution:
It is given in the problem that the weight of mass is 1kg and we need to find the equivalent mass in dynes.
The force has SI Newton and dyne is the cgs unit of force.
The weight of the 1kg on the earth is equal to,
$\Rightarrow F = m \times g$
Where force is F the mass of the object is m and the acceleration due to gravity is g.
$\Rightarrow F = m \times g$
$\Rightarrow F = 1 \times 9 \cdot 8$
$\Rightarrow F = 9 \cdot 8N$.
Now let us calculate the value of force in the cgs unit.
$\Rightarrow F = m \times g$
The mass in grams is equal to $1kg = 1000g$ and acceleration due to gravity in cgs unit is equal to,
$\Rightarrow g = 9 \cdot 8\dfrac{m}{{{s^2}}}$
Since, $1m = 100cm$
$\Rightarrow g = \left( {9 \cdot 8} \right) \times \left( {100} \right)\dfrac{{cm}}{{{s^2}}}$
$\Rightarrow g = 980\dfrac{{cm}}{{{s^2}}}$
The weight of the 1kg mass in dynes is equal to,
$\Rightarrow F = m \times g$
$\Rightarrow F = 1000 \times 980$
$\Rightarrow F = 9 \cdot 8 \times {10^5}dynes$.
The force in dynes is equal to $F = 9 \cdot 8 \times {10^5}dynes$.

The correct option for this problem is option A.

Note: It is advisable for students to remember the formula of the force as it is very useful in solving problems like these. The S I unit of force is equal to Newton in which the mass of the is in meters and acceleration is in$\dfrac{m}{{{s^2}}}$ but in cgs unit the mass is in grams and the acceleration is in$\dfrac{{cm}}{{{s^2}}}$.