In a new system of units on mass, 5 kg is unit of mass, 5 m is unit of length and 1 sec. is unit of time. Find the value of 5N force in new system.

1. Break Down the Problem

To find the value of 5 N (Newtons) of force in the new system of units, we first need to understand the definition of force in terms of mass, length, and time in SI units: $F = m \cdot a$ where $F$ is force in Newtons, $m$ is mass in kilograms, and $a$ is acceleration in meters per second squared.

2. Relevant Concepts

In SI units:

• Force (N) is defined as $1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2$.

We need to convert mass (kg) and length (m) into the new system of units provided:

• New unit of mass = 5 kg
• New unit of length = 5 m

3. Analysis and Detail

First, we convert 5 N into our new system of units:

1. In SI units, we have: $5 \, \text{N} = 5 \, \text{kg} \cdot \text{m/s}^2$

2. Now, using the new units, we express mass and length:

   • 1 kg in new units = $\frac{1}{5}$ units of mass
   • 1 m in new units = $\frac{1}{5}$ units of length

3. Substitute these into the equation: $5 \, \text{N} = 5 \cdot \left( \frac{1}{5} \, \text{units of mass} \cdot \frac{1}{5} \, \text{units of length}/\text{sec}^2 \right)$

4. Simplifying the right side: $5 \, \text{N} = 5 \cdot \left( \frac{1}{5} \cdot \frac{1}{5} \, \text{units of mass} \cdot \text{length}/\text{sec}^2 \right)$

4. Verify and Summarize

5. Calculate: $= 5 \cdot \frac{1}{25} \, \text{(units of mass) (length/s}^2\text{)} = \frac{5}{25} \text{ (units of mass) (length/s}^2\text{)} = \frac{1}{5} \, \text{(units of mass) (length/s}^2\text{)}$

Thus, the value of 5 N in the new system of units is expressed in terms of the new units of mass and length as $\frac{1}{5} \, \text{(new unit of mass) (new unit of length/s}^2\text{)}$.

Final Answer

The value of 5 N in the new system of units is $\frac{1}{5} \, \text{(new unit of mass) (new unit of length/s}^2\text{)}$.