A ball of correct diameter 3.761 cm is placed between the jaws of a screw gauge but it gives the diameter reading of 3.754 cm. When diameter of another ball is measured by the same screw gauge, its reading comes out to be 7.000 cm, correct diameter of the second ball is : (1) 7.007 cm (2) 6.993 cm (3) 7.000 cm (4) 7.754 cm

To determine the correct diameter of the second ball using the information provided, we first need to understand the error in the screw gauge measurements. The first ball has a known correct diameter of 3.761 cm, but the screw gauge reads it as 3.754 cm. This indicates that the screw gauge is consistently under-reading the diameter by a certain amount.

Calculating the Error

Let's calculate the error in the first measurement:

• Correct diameter of the first ball: 3.761 cm
• Measured diameter of the first ball: 3.754 cm
• Error = Measured diameter - Correct diameter = 3.754 cm - 3.761 cm = -0.007 cm

This shows that the screw gauge underestimates the diameter by 0.007 cm.

Applying the Error to the Second Measurement

Now, we apply this error to the second ball, which has a measured diameter of 7.000 cm. Since the screw gauge consistently under-reports the diameter by 0.007 cm, we can find the correct diameter of the second ball as follows:

• Measured diameter of the second ball: 7.000 cm
• Error: -0.007 cm
• Correct diameter = Measured diameter - Error = 7.000 cm - (-0.007 cm) = 7.000 cm + 0.007 cm = 7.007 cm

Conclusion on the Correct Diameter

Therefore, the correct diameter of the second ball is 7.007 cm. Among the options provided, the correct answer is:

• (1) 7.007 cm
• (2) 6.993 cm
• (3) 7.000 cm
• (4) 7.754 cm

Thus, the answer is (1) 7.007 cm.