The tension in the string is:

Options

A. 29.4 N
B. 39.2 N
C. 58.8 N
D. 88.2 N

Explanation

To find the tension in the string in the given arrangement, we can follow these steps:

### Step 1: Understand the Forces Acting on the Object
In the given scenario, we have an object of mass \( m \) hanging from a string. The forces acting on the object include:
- The gravitational force \( mg \) acting downward.
- The tension \( T \) in the string acting upward.
- The normal force \( N \) acting perpendicular to the surface.
- The frictional force \( f \) acting opposite to the direction of motion.

### Step 2: Break Down the Gravitational Force
The gravitational force can be broken down into two components:
- The component parallel to the surface: \( mg \sin \theta \)
- The component perpendicular to the surface: \( mg \cos \theta \)

Given that \( \theta = 37^\circ \), we can calculate:
- \( \sin 37^\circ = 0.6 \) (approximately)
- \( \cos 37^\circ = 0.8 \) (approximately)

Thus, we have:
- \( mg \sin 37^\circ = 0.6mg \)
- \( mg \cos 37^\circ = 0.8mg \)

### Step 3: Apply Newton's Second Law
For vertical equilibrium, the sum of the forces in the vertical direction must equal zero:
\[ T - mg \sin 37^\circ - f = 0 \]
Where \( f \) is the frictional force, which can be expressed as:
\[ f = \mu N \]
where \( \mu = 0.8 \) is the coefficient of friction.

### Step 4: Calculate the Normal Force
The normal force \( N \) can be expressed in terms of the gravitational force:
\[ N = mg \cos 37^\circ = 0.8mg \]

### Step 5: Substitute the Normal Force into the Frictional Force Equation
Now substitute \( N \) into the equation for friction:
\[ f = \mu N = 0.8 \times 0.8mg = 0.64mg \]

### Step 6: Substitute Back into the Force Equation
Now substitute \( f \) back into the equilibrium equation:
\[ T - mg \sin 37^\circ - 0.64mg = 0 \]
Substituting the value of \( mg \sin 37^\circ \):
\[ T - 0.6mg - 0.64mg = 0 \]
\[ T = 0.6mg + 0.64mg = 1.24mg \]

### Step 7: Calculate the Tension
Assuming \( g = 10 \, \text{m/s}^2 \) and \( m = 1 \, \text{kg} \) (for simplicity):
\[ T = 1.24 \times 10 \, \text{N} = 12.4 \, \text{N} \]

Thus, the tension in the string is \( \mathbf{12.4 \, N} \).

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