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Two masses m(1) and m(2) (m(1) gt m(2))...

Two masses `m_(1)` and `m_(2) (m_(1) gt m_(2))` are falling from the same height when same air resistance acts on them

A

`m_(1)` has more acceleration

B

`m_(1)` reaches the ground early

C

`m_(1)` has more velocity on striking the ground

D

all the above

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the forces acting on two masses, \( m_1 \) and \( m_2 \), as they fall under the influence of gravity and experience the same air resistance. ### Step-by-Step Solution: 1. **Identify Forces Acting on the Masses**: - The gravitational force acting on mass \( m_1 \) is \( F_{g1} = m_1 g \). - The gravitational force acting on mass \( m_2 \) is \( F_{g2} = m_2 g \). - Both masses experience the same air resistance \( F_r \). 2. **Write the Net Force Equations**: - For mass \( m_1 \): \[ F_{net1} = m_1 g - F_r \] - For mass \( m_2 \): \[ F_{net2} = m_2 g - F_r \] 3. **Apply Newton's Second Law**: - According to Newton's second law, \( F_{net} = m \cdot a \). - For mass \( m_1 \): \[ m_1 g - F_r = m_1 a_1 \quad \text{(1)} \] - For mass \( m_2 \): \[ m_2 g - F_r = m_2 a_2 \quad \text{(2)} \] 4. **Rearranging the Equations**: - Rearranging equation (1): \[ a_1 = \frac{m_1 g - F_r}{m_1} \] - Rearranging equation (2): \[ a_2 = \frac{m_2 g - F_r}{m_2} \] 5. **Comparing Accelerations**: - Since \( m_1 > m_2 \) and both experience the same air resistance \( F_r \), we can compare \( a_1 \) and \( a_2 \): - The term \( m_1 g \) will be greater than \( m_2 g \) because \( m_1 > m_2 \). - Thus, \( a_1 \) will be greater than \( a_2 \): \[ a_1 > a_2 \] 6. **Conclusion**: - Since \( a_1 > a_2 \), mass \( m_1 \) will accelerate faster than mass \( m_2 \). - Therefore, mass \( m_1 \) will reach the ground before mass \( m_2 \) and will have a greater velocity upon impact. ### Final Answer: All the statements regarding the scenario are correct. Thus, the correct option is that \( m_1 \) reaches the ground first and has a greater velocity upon impact. ---
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