Question

A man is standing on a weighing machine kept on the floor of an elevator. The ratio of measured weight of the man when elevator is at rest and when it is moving with downward acceleration a is 3 : 2. The value of a is :

A. g/3
B. 3g/2
C. g
D. 2g/3

Answer 1

The value of a is 2g/3.

Step-by-step explanation:

The ratio of the measured weight of a man when the elevator is at rest and when it is moving with a downward acceleration is 3:2. Let's assume the weight of the man when the elevator is at rest is W.

When the elevator is moving downwards with acceleration a, the net force acting on the man is F = W - mg, where m is the mass of the man and g is the acceleration due to gravity (approximately 9.8 m/s^2). According to Newton's second law, F = ma. Therefore, we have:

W - mg = ma

To find the value of a, we can use the given ratio of weights:

W / (W - mg) = 3 / 2

Cross multiplying and simplifying:

2W = 3(W - mg)

2W = 3W - 3mg

W = 3mg

Substituting this back into the equation W - mg = ma:

3mg - mg = ma

2mg = ma

a = 2g/3