The weight of man in a stationary lift is w ₁ and when it is moving downwards with uniform acceleration ' a ' is w₂ . If the ratio w ₁: w ₂=4: 3 , then the value of ' a ' is ( g = acceleration due to gravity)

Step-by-step solution

Let m represent the man's mass and g the acceleration due to gravity. When stationary, the apparent weight equals the actual weight: w₁ = mg . With downward acceleration a , the apparent weight becomes w₂ = m(g - a) . Given w₁ : w₂ = 4 : 3 , so w₁ w₂ = 4 3 . Substituting, mg m(g - a) = 4 3 . Simplification yields g g - a = 4 3 , and cross-multiplying gives 3g = 4(g - a) . Solving this, 3g = 4g - 4a , so 4a = g , hence a = g 4 . Option B is correct.