A block of mass `M` is pulled along a horizontal frictionless surface by a rope of mass `m` . Force F is applied at one end of rope. The force which the rope exerts on the block is:

Options

A. F/(M+m)
B. F should be equal to the weight of A and B
C. FM/(m+M)
D. Zero

Explanation

To solve the problem, we need to determine the force that the rope exerts on the block when a force \( F \) is applied to the rope. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the system
We have a block of mass \( M \) and a rope of mass \( m \) on a horizontal frictionless surface. A force \( F \) is applied to one end of the rope. The entire system (rope + block) will accelerate due to the applied force.

### Step 2: Calculate the total mass of the system
The total mass of the system can be expressed as:
\[ m_{\text{total}} = M + m \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force acting on the system is equal to the total mass of the system multiplied by its acceleration:
\[ F_{\text{net}} = m_{\text{total}} \cdot a \]
Here, the net force \( F \) is the only force acting on the system. Therefore:
\[ F = (M + m) \cdot a \]

### Step 4: Solve for acceleration
Rearranging the equation to solve for acceleration \( a \):
\[ a = \frac{F}{M + m} \]

### Step 5: Determine the force exerted by the rope on the block
The force exerted by the rope on the block can be calculated using the block's mass and the acceleration we just found. According to Newton's second law:
\[ F_{\text{rope on block}} = M \cdot a \]
Substituting the expression for acceleration:
\[ F_{\text{rope on block}} = M \cdot \left(\frac{F}{M + m}\right) \]
Thus, we have:
\[ F_{\text{rope on block}} = \frac{M \cdot F}{M + m} \]

### Conclusion
The force that the rope exerts on the block is:
\[ \boxed{\frac{M \cdot F}{M + m}} \]