Question

The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as:
(A) $m (1 - \dfrac{a}{g})$
(B) $m (1 + \dfrac{a}{g})$
(C) m
(D) zero

Answer 1

The difference in mass and weight of a body is that mass is the matter constitution of that body and weight is the gravitational force that the body experiences and exerts due its mass. Mass has units in kilograms and weight can be expressed in Newtons (N).

Complete answer:
We simply write down all the forces on the block first,
(1) Normal reaction upwards of the surface of the lift on the mass.
(2) Downwards force of the mass on the lift.
(3) Pseudoforce downwards that mass experiences due to the motion of the lift upwards.
The forces can be balanced as:
R = mg + ma
This normal reaction value is the new weight of the body.
Now, in our question we are given that the mass of the body is m and again we are asked to find the mass. Now, mass of a body remains constant no matter wherever one goes. The mass of the body remains the same; it is a physical property of the body.

Therefore, the mass of the body is m and the correct answer is option (C).

Additional information:
When the lift is accelerating, the mass inside it is present in a non-inertial frame of reference. Newton's laws are not valid in a non-inertial frame. We cannot draw free-body diagrams mentioning all forces in a single picture of motion for the body as there is a pseudo force on the mass due to acceleration of the lift upwards. This cannot be drawn together with the real forces acting on the body. Either the picture has to be made in the accelerating frame or the stationary frame.

Note:
The mass of anybody stays constant no matter whatever frame we choose to describe our system in. One can put the same mass on the moon or on Earth or even in a rotating frame, the value of mass will always be the same in all the frames.