A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F. The kinetic energy of the block increases by 20J in 1s.

Options

A. the tension in the string is Mg
B. The tension is the string is F
C. The work done by the tension on the block is 20 J in the above 1s.
D. the work done by the force of gravity is -20J in the above 1s.

Answer

To solve the problem, we need to analyze the situation involving the block, the pulley, and the forces acting on the block. Here's a step-by-step solution:

### Step 1: Understand the System
We have a block of mass \( M \) hanging over a smooth and light pulley. The other end of the string is being pulled by a constant force \( F \). The block's kinetic energy increases by 20 J in 1 second.

### Step 2: Work-Energy Principle
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Therefore, if the kinetic energy of the block increases by 20 J in 1 second, the work done on the block in that time is also 20 J.

### Step 3: Calculate the Work Done
The work done \( W \) can be expressed as:
\[ W = F_{\text{net}} \cdot d \]
where \( F_{\text{net}} \) is the net force acting on the block and \( d \) is the distance moved by the block in 1 second.

### Step 4: Identify Forces Acting on the Block
The forces acting on the block are:
1. The gravitational force \( Mg \) acting downwards.
2. The tension \( T \) in the string acting upwards.

Since the pulley is smooth and light, we can assume that the tension \( T \) is equal to the force \( F \) applied at the other end of the string.

### Step 5: Set Up the Equation
Using Newton's second law, we can write the equation of motion for the block:
\[ F - Mg = Ma \]
where \( a \) is the acceleration of the block.

### Step 6: Relate Work Done to Forces
The net work done on the block can also be expressed as:
\[ W = (T - Mg) \cdot d \]
Since we know \( W = 20 \, \text{J} \), we can substitute:
\[ 20 = (F - Mg) \cdot d \]

### Step 7: Analyze the Situation
Since the kinetic energy is increasing, the block is accelerating. This means that \( F \) must be greater than \( Mg \) for the block to move upwards and gain kinetic energy.

### Step 8: Conclusion
From our analysis, we can conclude that:
- The work done by the applied force \( F \) is responsible for the increase in kinetic energy.
- The tension in the string is equal to the force \( F \) applied.

### Final Answer
The correct interpretation of the forces and work done leads us to conclude that the work done by the applied force \( F \) is 20 J, which results in the increase in kinetic energy of the block.

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