A block of mass 2 kg 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 = 40 N. The kinetic energy of the particle increases 40 J in a given interval of time. Then, `(g = 10 m//s^(2))`

Options

A. tension in the string is 40 N
B. displacement of the block in the given interval of time is 2 m
C. work done by gravity is `-20 J`
D. work done by tension is 80 J

Answer

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

### Step 1: Identify the forces acting on the block
The block of mass \( m = 2 \, \text{kg} \) is hanging and is subjected to two forces:
1. The gravitational force acting downwards: \( F_g = m \cdot g = 2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20 \, \text{N} \)
2. The tension \( T \) in the string, which is equal to the force \( F = 40 \, \text{N} \) pulling the other end of the string.

### Step 2: Calculate the net force acting on the block
The net force \( F_{net} \) acting on the block can be calculated as:
\[ F_{net} = T - F_g = 40 \, \text{N} - 20 \, \text{N} = 20 \, \text{N} \]

### Step 3: Calculate the acceleration of the block
Using Newton's second law, \( F = m \cdot a \), we can find the acceleration \( a \) of the block:
\[ a = \frac{F_{net}}{m} = \frac{20 \, \text{N}}{2 \, \text{kg}} = 10 \, \text{m/s}^2 \]

### Step 4: Relate the change in kinetic energy to work done
The change in kinetic energy \( \Delta KE \) is given as \( 40 \, \text{J} \). According to the work-energy theorem, the work done \( W \) on the block is equal to the change in kinetic energy:
\[ W = \Delta KE = 40 \, \text{J} \]

### Step 5: Calculate the distance moved by the block
The work done can also be expressed as:
\[ W = F_{net} \cdot d \]
where \( d \) is the distance moved by the block. Rearranging gives:
\[ d = \frac{W}{F_{net}} = \frac{40 \, \text{J}}{20 \, \text{N}} = 2 \, \text{m} \]

### Final Answer
The distance moved by the block is \( 2 \, \text{m} \).

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