A body hanged by a rope in a lift which is moving upward with a constant acceleration of $ 0.2 \, \text{m/s}^2 $. The tension in the rope is 80 N. Find the mass of the body.
Show Hint
- 10 kg
8 kg
- 40 kg
- 80 kg
The Correct Option is B
Solution and Explanation
The forces acting on the body are: 1. The tension \( T \) in the rope, which acts upwards. 2. The weight of the body \( W = mg \), which acts downwards. 3. The force due to the acceleration of the lift \( F = ma \), where \( a = 0.2 \, \text{m/s}^2 \) is the acceleration of the lift.
The net force on the body is the difference between the upward tension and the downward weight, and it equals the mass times the acceleration of the lift: \[ T - mg = ma \] Substitute the known values: \[ 80 - m(9.8) = m(0.2) \] Simplify the equation: \[ 80 = m(9.8 + 0.2) \] \[ 80 = m(10) \] \[ m = \frac{80}{10} = 8 \, \text{kg} \]
Thus, the mass of the body is \( 8 \, \text{kg} \).
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