The pitch and the number of divisions, on the circular scale for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 division below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 4.5 mm and 48 respectively, the thickness of the sheet is:

To find the thickness of the sheet using the given information, we can follow these steps:

Step 1: Determine the zero error of the screw gauge. The zero of the circular scale lies 3 divisions below the mean line when the screw gauge is fully tightened without any object. This means that there is a zero error of -3 divisions.

Step 2: Calculate the effective reading on the circular scale. The effective reading on the circular scale is the actual reading minus the zero error. In this case, the actual reading on the circular scale is 48 divisions. So, the effective reading is 48 - (-3) = 51 divisions.

Step 3: Calculate the total reading on the screw gauge. The total reading on the screw gauge is the sum of the main scale reading and the effective reading on the circular scale. The main scale reading is given as 4.5 mm, which is equivalent to 4.5 * 100 = 450 divisions. So, the total reading is 450 + 51 = 501 divisions.

Step 4: Calculate the pitch of the screw gauge. The pitch is given as 0.5 mm, which is equivalent to 0.5 * 100 = 50 divisions.

Step 5: Calculate the thickness of the sheet. The thickness of the sheet can be calculated using the formula: Thickness = (Total reading - Zero error) * Pitch Substituting the values, we get: Thickness = (501 - (-3)) * 0.5 Thickness = 504 * 0.5 Thickness = 252 mm

Therefore, the thickness of the sheet is 252 mm.