Question

A student is weighing an object using a spring balance, which shows a reading of $5\,kg$. If the body loses grip and the spring balance along with the object falls under gravity, then the weight as measured by the spring balance and mass of the object are respectively. ($g = 10\,m/{s^2}$ )
A) $0\,N$ , $0\,kg$
B) $50\,N$ , $5\,kg$
C) $0\,N$ , $2.5\,kg$
D) $0\,N$ , $5\,kg$

Answer 1

We know that weight is the product of mass and acceleration due to gravity. In the case of free fall the spring will exert a normal reaction force on the object the effective weight will be the difference between actual weight and the normal reaction force.

Complete step by step solution:
It is given that when a student weighs an object using spring balance the reading shown is $5\,kg$ .
We are asked to find the weight and mass of the object when the spring balance falls with the object under gravity.
It is given that acceleration due to gravity is
$g = 10m/{s^2}$
Since the spring balance reads $5\,kg$
Mass of the object$= 5\,kg$
We know that weight is mass multiplied by acceleration due to gravity
$w = mg$
Thus, the weight of object when spring balance ls fixed is
$w = m \times g = 5 \times 10 = 50N$
When spring balance falls down along with the object the effective weight is
$w' = w - ma$
Here $ma$ is the normal reaction force exerted by the spring balance and since the spring is also falling under gravity the value of a is the same as g .
$a = g$
$w' = w - mg$
On substituting the values we get ,
$\therefore w' = 50 - 5 \times 10$
$\therefore w' = 0\,N$
So, the effective weight of the object will be zero when the spring along with the object is falling under gravity.
But mass will remain constant. Mass will not change when it falls. So when the spring balance falls
the mass of object will still be $5kg$

Thus, the correct answer is option D.

Note: Remember that mass is the amount of matter contained in a body. When the object is falling freely along with the spring the weight which is the product of mass and acceleration due to gravity becomes effectively zero because it is cancelled by equal normal reaction force exerted by the spring. But there is no change in the amount of substance when it falls. So, mass remains the same.