A balloon starting from rest ascends vertically with uniform acceleration to a height of 100m is 10s. The force on the bottom of the balloon by a mass of 50 kg us (`g=ms^(-2)`)

Options

A. 100 N
B. 300 N
C. 600 N
D. 400 N

Explanation

To solve the problem step by step, we need to find the force exerted on the bottom of the balloon by a mass of 50 kg as it ascends with uniform acceleration. Here’s how we can approach this:

### Step 1: Understand the Given Information
- Height (h) = 100 m
- Time (t) = 10 s
- Mass of the balloon (m) = 50 kg
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Determine the Acceleration of the Balloon
Since the balloon starts from rest and ascends to a height of 100 m in 10 seconds, we can use the second equation of motion:
\[ h = ut + \frac{1}{2} a t^2 \]
Where:
- \( u \) = initial velocity = 0 (since it starts from rest)
- \( a \) = acceleration
- \( t \) = time

Substituting the known values:
\[ 100 = 0 \cdot 10 + \frac{1}{2} a (10^2) \]
\[ 100 = \frac{1}{2} a (100) \]
\[ 100 = 50a \]
\[ a = \frac{100}{50} = 2 \, \text{m/s}^2 \]

### Step 3: Calculate the Total Force Acting on the Balloon
The total force \( F \) acting on the balloon can be calculated using the formula:
\[ F = mg + ma \]
Where:
- \( F \) = total force
- \( m \) = mass of the balloon = 50 kg
- \( g \) = acceleration due to gravity = 10 m/s²
- \( a \) = acceleration of the balloon = 2 m/s²

Substituting the values:
\[ F = 50 \cdot 10 + 50 \cdot 2 \]
\[ F = 500 + 100 \]
\[ F = 600 \, \text{N} \]

### Final Answer
The force on the bottom of the balloon by a mass of 50 kg is **600 N**.

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