Measurement of Length — Prelims Questions

A student measures the diameter of a small steel ball using a screw gauge. The pitch of the screw gauge is $1,\text{mm}$ and there are 100 divisions on the circular scale. The main scale reading is $5,\text{mm}$ and the 58th division on the circular scale coincides with the main line. The screw gauge has a positive zero error of $0.03,\text{mm}$. What is the corrected diameter of the steel ball?

A Vernier caliper has 10 divisions on its Vernier scale, which coincide with 9 divisions on the main scale. Each main scale division (MSD) is $1,\text{mm}$. When the jaws are closed, the 7th division of the Vernier scale coincides with a main scale division, and the zero of the Vernier scale is to the left of the zero of the main scale. While measuring a length, the main scale reading is $3.5,\text{cm}$ and the 4th Vernier division coincides. What is the actual length measured?

The diameter of a sphere is measured to be $2.745,\text{cm}$ using a Vernier caliper. If the least count of the Vernier caliper is $0.01,\text{cm}$, what is the maximum possible percentage error in the measurement?

A star is $4.2$ light-years away from Earth. If $1$ light-year is approximately $9.46 \times 10^{15},\text{m}$, what is the distance of the star in kilometers?

Which of the following statements about the precision and accuracy of length measurements is correct?

The parallax angle of a distant star is measured to be $0.5''$ (arcseconds). If the baseline used for observation is the diameter of Earth's orbit around the Sun, which is approximately $3 \times 10^{11},\text{m}$, what is the distance to the star? (Given: $1'' = 4.85 \times 10^{-6},\text{radians}$)