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A person holds a spring balance with a m...

A person holds a spring balance with a mass `m` hanging from it goes up and up in a helicopter, then reading of weight of body as indicated by spring balance will.

A

be increasing

B

be decreasing

C

first increase and then decrease

D

remain the same.

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AI Generated Solution

The correct Answer is:
To solve the problem of how the reading of the spring balance changes when a mass `m` is hanging from it in a helicopter that is ascending, we can analyze the forces acting on the mass and apply Newton's laws of motion. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Mass**: - The mass `m` experiences two forces: - The gravitational force acting downward, which is \( F_g = mg \) (where \( g \) is the acceleration due to gravity). - The tension \( T \) in the spring balance acting upward. 2. **Consider the Acceleration of the Helicopter**: - When the helicopter ascends, it accelerates upward. Let’s denote the upward acceleration of the helicopter as \( a \). 3. **Apply Newton's Second Law**: - According to Newton's second law, the net force acting on the mass is equal to the mass times its acceleration. - The net force \( F_{net} \) acting on the mass can be expressed as: \[ F_{net} = T - mg \] - Since the helicopter is accelerating upward, the net force is also given by: \[ F_{net} = ma \] 4. **Set Up the Equation**: - Setting the two expressions for net force equal gives: \[ T - mg = ma \] 5. **Solve for Tension (T)**: - Rearranging the equation to solve for the tension \( T \): \[ T = mg + ma \] - This can be factored as: \[ T = m(g + a) \] 6. **Interpret the Result**: - The reading on the spring balance (which measures the tension) will be \( T = m(g + a) \). - This indicates that the reading of the weight of the body as indicated by the spring balance will increase when the helicopter ascends, as it is the sum of the gravitational force and the additional force due to the upward acceleration. ### Final Answer: The reading of the weight of the body as indicated by the spring balance will increase and be equal to \( m(g + a) \).

To solve the problem of how the reading of the spring balance changes when a mass `m` is hanging from it in a helicopter that is ascending, we can analyze the forces acting on the mass and apply Newton's laws of motion. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Mass**: - The mass `m` experiences two forces: - The gravitational force acting downward, which is \( F_g = mg \) (where \( g \) is the acceleration due to gravity). - The tension \( T \) in the spring balance acting upward. ...
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