Question : In a particular system, the units of length, mass, and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to:
Option 1: 0.1 N
Option 2: 1 N
Option 3: 10 N
Option 4: 100 N
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Correct Answer: 0.1 N
Solution : The correct option is 0.1 N .
The units of length, mass and time in the provided system are 10 cm, 10 g, and 0.1 s, respectively. The formula a = v/t, where v is the change in velocity and t is the change in time, may be used to compute the unit of acceleration. The unit of acceleration is thus:
v/t = (10 cm/s)/(0.1 s) = 100 cm/s
2
where a = v/t.
We must divide this unit by 100 to get the conventional unit of acceleration or m/s
2
.
Therefore, 1 m/s
2
/100 = 0.01 m/s
2
serves as the unit of acceleration in this system F = ma = (10 g) * (0.01 m/s
2
) = 0.1 N
As a result, the system's unit of force is 0.1 N.
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