A body of weight 40 kg rests on a rough horizontal plane, whose coefficient of friction is `0*25`. The least force which acting horizontal would move the body is

Options

A. 10 kg wt
B. 2 kg wt
C. 30 kg wt
D. 40 kg wt

Answer

To find the least force required to move a body resting on a rough horizontal plane, we can use the formula for the force of friction. The force of friction (F_friction) is given by:

\[ F_{\text{friction}} = \mu \cdot N \]

where:
- \( \mu \) is the coefficient of friction,
- \( N \) is the normal force acting on the body.

### Step 1: Calculate the Normal Force (N)
The normal force for a body resting on a horizontal surface is equal to the weight of the body. The weight (W) can be calculated using the formula:

\[ W = m \cdot g \]

where:
- \( m \) is the mass of the body (40 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

Calculating the weight:

\[ W = 40 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 392.4 \, \text{N} \]

Thus, the normal force \( N \) is:

\[ N = W = 392.4 \, \text{N} \]

### Step 2: Calculate the Force of Friction (F_friction)
Now, we can calculate the force of friction using the coefficient of friction \( \mu = 0.25 \):

\[ F_{\text{friction}} = \mu \cdot N = 0.25 \cdot 392.4 \, \text{N} \]

Calculating the force of friction:

\[ F_{\text{friction}} = 0.25 \cdot 392.4 \, \text{N} = 98.1 \, \text{N} \]

### Step 3: Determine the Least Force Required to Move the Body
The least force (F) required to overcome friction and move the body is equal to the force of friction:

\[ F = F_{\text{friction}} = 98.1 \, \text{N} \]

### Final Answer
The least force which acting horizontally would move the body is **98.1 N**.

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