Question

A block of mass $m$ is suspended from the ceiling of a lift by an inextensible string. When the lift moves upward with an acceleration of $0.2\ \text{m s}^{-2}$, the tension is $80\ \text{N}$. Then the mass of the block is:

• A. 1 kg
• B. 2 kg
• C. 8 kg
• D. 6 kg
• E. 4 kg

Hint:

Apparent weight increases when a lift accelerates upwards ($T = m(g+a)$) and decreases when accelerating downwards ($T = m(g-a)$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves Newton's second law of motion applied to a non-inertial (accelerating) frame of reference. When a lift accelerates upwards, the apparent weight of the object inside it increases, resulting in a tension greater than its actual weight.
Step 2: Key Formula or Approach:
1. Draw a free-body diagram for the block. The forces acting on it are: - Tension (T) acting upwards. - Gravitational force (weight, mg) acting downwards. 2. Apply Newton's second law, \( F_{net} = ma \). The net force is the vector sum of all forces. \[ T - mg = ma \] where 'a' is the upward acceleration of the lift. Step 3: Detailed Explanation:
We are given: - Tension, \( T = 80 \text{ N} \) - Upward acceleration, \( a = 0.2 \text{ m/s}^2 \) We need to find the mass, m. The equation of motion is: \[ T = mg + ma = m(g+a) \] To solve for m, we need the value of the acceleration due to gravity, g. Let's assume \( g = 9.8 \text{ m/s}^2 \) as is standard unless specified otherwise. \[ 80 = m(9.8 + 0.2) \] \[ 80 = m(10) \] \[ m = \frac{80}{10} = 8 \text{ kg} \] This calculation perfectly matches option (C). The question implicitly requires the use of g = 9.8 m/s\(^2\). Step 4: Final Answer:
The mass of the block is 8 kg.