A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is:
A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is:
zero
75 kg
84.8 kg
65.2 kg
The Correct Option is A
Solution and Explanation
The correct option is: (A) zero.
(i) The man's mass is m = 70 kg. The acceleration is a = 0. By applying Newton's second law of motion, the equation of motion becomes: R - mg = ma Here, ma represents the net force acting on the man. Since the lift moves at a uniform speed (a = 0), the equation simplifies to: R = mg = 70 × 10 = 700 N Hence, the reading on the weighing scale = 700 g = 700 / 10 = 70 kg.
(ii) The man's mass is m = 70 kg. The acceleration is a = 5 m/s² downward. Using Newton's second law of motion, we can rewrite the equation as: mg - R = ma Substituting the values: R = m(g - a) = 70(10 - 5) = 70 × 5 = 350 N Therefore, the reading on the weighing scale = 350 g = 350 / 10 = 35 kg.
(iii) The man's mass is m = 70 kg. The acceleration is a = 5 m/s² upward. Applying Newton's second law of motion gives us: R - mg = ma Substituting the values: R = m(g + a) = 70(10 + 5) = 70 × 15 = 1050 N Hence, the reading on the weighing scale = 1050 g = 1050 / 10 = 105 kg.
(iv) When the lift moves freely under gravity, a = g. By Newton's second law of motion, the equation becomes: mg - R = ma Substituting a = g: R = m(g - g) = 0 In this case, the reading on the weighing scale = 0 g = 0 kg. The man will experience a state of weightlessness.
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.