Multiplication & Division of Errors

Q. The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

1. $3\%$
2. $5\%$
3. $6\%$
4. $8\%$

Q. The length of cylinder is measured with a metre rod having least count $0.1\text{cm}$. Its diameter is measured with vernier caliper having least count $0.01\text{cm}$. Given that length is $5.0\text{cm}$ and diameter is $4.0\text{cm}$. The percentage error in the calculated value of the volume will be

1. $1.5\%$
2. $2.5\%$
3. $3.5\%$
4. $4\%$

Q. If radius of the sphere is (5.3 $\pm$ 0.1)cm. Then percentage error in its volume will be

1. 3+6.01 $\times \frac{100}{5.3}$
2. $\frac{1}{3}\times$ 0.01 $\times \frac{100}{5.3}$
3. $\left(\frac{3\times 0.1}{5.3}\right)\times 100$
4. $\frac{0.1}{5.3}\times 100$

Q. Length $l$ and Acceleration due to gravity $g$ are measured with $\pm 6\%$ and $\pm 4\%$ errors respectively. The percentage error in determination of the Time period of a simple pendulum will be,

1. $\pm 7\%$
2. $\pm 2\%$
3. $\pm 5\%$
4. $\pm 4\%$

Q. Side of an equilateral triangle is measured as $3.6\pm .06$ cm, find percentage error in area of triangle

1. 4.2 %
2. 2.8 %
3. 3.4 %
4. 1.7 %