A block of mass m is attached to a string and suspended inside an otherwise empty box of mass M. The box rests on a scale that measures the system’s weight. (a) If the string breaks, does the reading on the scale change? Explain your reasoning. (b) Assume that the string breaks and the mass m falls with constant acceleration g. Find the magnitude and direction of the acceleration of the center of mass of the box–block system. (c) Using the result from (b), determine the reading on the scale while m is in free-fall.
tu answer kar na
(a) If the string breaks, the reading on the scale does not change. The reason for this is that the scale measures the weight of the entire system, which includes both the block and the box. When the string breaks, the block falls freely and the box remains stationary. Since the weight of the box is still supported by the scale, its reading will remain unchanged. The weight of the block is no longer acting on the scale, but this does not affect the reading since the scale only measures the total weight of the system.
(b) When the string breaks, the block falls with constant acceleration g. Since there are no external forces acting horizontally on the system, the acceleration of the center of mass of the box-block system will also be g, directed vertically downwards. This is because the force of gravity acts equally on both the block and the box, and since the mass of the box is much larger than the mass of the block, the acceleration of the center of mass is approximately equal to the acceleration due to gravity.
(c) While the block is in free-fall, the reading on the scale will be equal to the weight of the box only. This is because the block is no longer supported by the string and its weight is no longer acting on the scale. Thus, the reading on the scale will be M multiplied by the acceleration due to gravity, which is equal to M * g.