Question

Stone tied at one end of light string is whirled round a vertical circle. If the difference between the maximum and minimum tension experienced by the string wire is $ 2kg $ $ wt $ , then the mass of the stone must be.

Answer 1

Hint :In physics, mass is a numerical measure of inertia, which is a basic property of all matter. It is, in essence, a body of matter's resistance to a change of speed or location caused by the application of a force. The smaller the shift caused by an applied force, the greater the mass of the body.

Complete Step By Step Answer:
From the question, we know that a stone is whirled around a vertical circle with one end of a light string tied to it. The mass of the stone must be $ 2kg $ $ wt $ if the difference between the highest and minimum tension experienced by the string is $ 2kg $ $ wt $ .
 $ {T_{\max }} - {T_{\min }} = 2kg $ weight
Using the relation tension of maximum and minimum we get,
The least velocity required for an object to rotate in a vertical plane is $ {v_1} = 5gr $ .
So, at the bottom point, $ {T_{\max }} = \dfrac{{mv_1^2}}{r} + mg = 6mg $
At top-most point velocity is $ {v_2} = gr $ .
So, $ {T_{\min }} = \dfrac{{mv_2^2}}{r} - mg = 0 $
 $ {T_{\max }} - {T_{\min }} = 6mg $
From both equations we get
 $ 2 \times g = 6 \times m \times g $
 Or $ 6 \times m = 2 $
 $ m = \dfrac{2}{6} \\
  m = \dfrac{1}{3} \\ $
Therefore, Mass of the stone is $ \dfrac{1}{3}kg $

Note :
Negative mass does not exist, but heavy things still come back, as fascinating as it might be. Second, gravitational fields can never be protected, obscured, or cancelled due to the absence of negative mass. Weight, on the other hand, comes in both positive and negative forms. Weight is a vector value, so it can be positive or negative, and it can be positive or negative with respect to reference.