A body of mass 4 kg weighs 4.8 kg when suspended in a moving lift. The acceleration of the lift is

Options

A. `9.80 ms^(-2)` downwards
B. `9.80ms^(-2)` upwards
C. `1.96 ms^(-1)` downwards
D. `1.96 ms^(-2)` upwards

Answer

To find the acceleration of the lift, we can use the concept of apparent weight and the equations of motion. Here’s the step-by-step solution:

### Step 1: Understand the Problem
We have a body of mass \( m = 4 \, \text{kg} \) that weighs \( 4.8 \, \text{kg} \) when suspended in a moving lift. We need to find the acceleration of the lift.

### Step 2: Convert Weight to Force
The weight of the body when suspended in the lift can be converted to force using the formula:
\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \, (g) \]
Given that the weight is \( 4.8 \, \text{kg} \), we can calculate the force:
\[ F = 4.8 \, \text{kg} \times 10 \, \text{m/s}^2 = 48 \, \text{N} \]

### Step 3: Apply Newton's Second Law
When the lift is accelerating, the apparent weight (normal force \( N \)) can be expressed as:
\[ N = mg + ma \]
Where:
- \( N \) is the normal force (apparent weight),
- \( m \) is the mass of the body,
- \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)),
- \( a \) is the acceleration of the lift.

### Step 4: Set Up the Equation
From the previous steps, we can set up the equation:
\[ 48 \, \text{N} = (4 \, \text{kg} \times 10 \, \text{m/s}^2) + (4 \, \text{kg} \times a) \]
This simplifies to:
\[ 48 = 40 + 4a \]

### Step 5: Solve for Acceleration \( a \)
Now, we can solve for \( a \):
\[ 48 - 40 = 4a \]
\[ 8 = 4a \]
\[ a = \frac{8}{4} = 2 \, \text{m/s}^2 \]

### Conclusion
The acceleration of the lift is \( 2 \, \text{m/s}^2 \).

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