Addition & Subtraction of Errors

Q. If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

1. $(0.94\pm 0.03)\text{cm}$
2. $(0.94\pm 0.01)\text{cm}$
3. $(0.94\pm 0.02)\text{cm}$
4. $(0.94\pm 0.04)\text{cm}$

Q. An experiment measures quantities $a,b$, and $c$ and then $X$ is calculated from $X=\frac{a^{1/2}{b}^2}{c^3}$. If the percentage errors in $a,b$ and $c$ are $\pm 1\%,\pm 3\%$, and $\pm 2\%$, respectively, then the percentage error in $X$ can be

1. $\pm 4\%$
2. $\pm 1\%$
3. $\pm 12.5\%$
4. $\pm 7\%$

Q. Time period of 10 oscillations of a simple pendulum is found to be 20 sec by a stopwatch of resolution 0.25 sec. Length of the string is measured to be 30 cm by a scale of least count 0.1 cm. Percentage error in measurement of acceleration due to gravity g by simple pendulum is? $T=2\pi \sqrt{\frac{l}{g}}$

Q. A physical quantity $Q$ is calculated according to the expression $Q=\frac{A^3{B}^3}{C\sqrt{D}}$. If percentage errors in $A,B,C,D$ are $2\%,1\%,3\%$ and $4\%$ respectively, what is the percentage error in $Q$?

1. $\pm 8$%
2. $\pm 10$%
3. $\pm 14$%
4. $\pm 12$%

Q. Consider a vernier caliper. Least count of main scale is $1mm$. There are 20 equispaced marks on vernier scale. When nothing is put between the jaws, zero of main scale lies between zero and first division of vernier scale and 15th division of vernier exactly coincide with one of the main scale division. When zero of vernier is matched with zero of main scale, 20th division of vernier exactly coincides with 25th division of main scale. To measure the side of a cuboid, it is kept between the jaws of vernier caliper, it is now observed that 18th division of vernier exactly coincides with 32th division of main scale. Choose the correct option(s).

1. Least count of vernier scale is $0.25mm$
2. Zero error is $-0.25mm$
3. Side of cuboid is $10.25mm$
4. When nothing is put between the jaws, zero of main scale lies between zero and first division of vernier scale and 15th division of vernier exactly coincide with one of the main scale division.This main scale division was 17th division of main scale.

Q. Volume of a cylindrical wire is measured with the help of a simple scale with 10 divisions per centimeter to measure length and a screw gauge with 100 divisions on circular scale with a pitch of 1 mm to measure the diameter. If length is 20 cm and diameter is 1 mm, then percentage error in volume is

1. 5%
2. 2.5%
3. 10%
4. 20%

Q. A physical quantity $P$ depends on other physical quantities $\alpha ,\beta ,\gamma$ as $P=\frac{{\alpha }^2{\beta }^3}{{\gamma }^4}$ where $\alpha ,\beta ,$ and $\gamma$ are known to have maximum percentage errors of $1\%,2\%$ and $1\%$ respectively , then maximum percentage error in $P$ would be

1. $4\%$
2. $10\%$
3. $12\%$
4. $6\%$

Q. A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

1. 7%
2. 8%
3. 9%
4. 5%

Q. In an experiment, the period of oscillation of a simple pendulum was observed to be $2.63s$, $2.56s$, $2.42s,2.71s$, and $2.80s$. The mean absolute error is:

1. $0.11s$
2. $0.12s$
3. $0.13s$
4. $0.14s$

Q. A student measured the diameter of a small steel ball using a screw gauge of least count $0.001cm.$ The main scale reading is $5mm$ and zero of circular scale division coincides with $25$ divisions above the reference level. If screw gauge has a zero error of -$0.004cm,$ the correct diameter of the ball is

1. $0.529cm$
2. $0.521cm$
3. $0.525cm$
4. $0.053cm$

Q. Two full turns of the circular scale of a screw gauge covers a distance of $1mm$ on its main scale. The total number of divisions on the circular scale is $50$. Further, it is found that the screw gauge has a zero error of $-0.03mm$. While measuring the diameter of a thin wire, a student notes the main scale reading of $3mm$ and the number of circular scale divisions in line with the main scale as $35$. The diameter of the wire is:

1. $3.32mm$
2. $3.73mm$
3. $3.67mm$
4. $3.38mm$

Q.

The density of a cube is measured by measuring its mass and the length of the sides. If the maximum error in the measurements of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be

1. $7\%$

2. $9\%$

3. $12\%$

4. $13\%$

Q. The volume of two bodies are measured to be $V_1=(10.20\pm 0.02){\text{cm}}^3$ and $V_2=(6.40\pm 0.01){\text{cm}}^3$.
The difference in volume with appropriate significant figures is

1. $(3.80\pm 0.04){\text{cm}}^3$
2. $(3.80\pm 0.01){\text{cm}}^3$
3. $(3.80\pm 0.03){\text{cm}}^3$
4. $(3.80\pm 0.02){\text{cm}}^3$

Q. In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0.25cm$. There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is:

1. $0.0430cm$
2. $0.4300cm$
3. $0.3150cm$
4. $0.2150cm$

Q. The diameter of a wire as measured by screw gauge was found to be $2.620,2.625,2.628and2.626cm$. Calculate mean absolute error.

1. $0.3$
2. $0.03$
3. $0.003$
4. $0.025$

Q.

The density of a cube is measured by measuring the mass and length of its side. If the maximum errors in the measurement of its mass and length are $3\%$ and $2\%$ respectively, the maximum error in the measurement of density would be:

Q. The period of oscillation of a simple pendulum in the experiment is recorded as $2.63s,2.56s,2.42s,2.71s$ and $2.80s$. Find the average absolute error.

Q. The number of circular divisions of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is:

1. 2.25 mm
2. 2.20 mm
3. 1.20 mm
4. 1.25 mm

Q. The circular divisions of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is :

1. $1.20mm$
2. $2.20mm$
3. $2.25mm$
4. $1.25mm$

Q. A screw gauge of pitch $1$mm has a circular scale divided into $100$ divisions. The diameter of a wire is to measured by above said screw gauge. The main scale reading is $1$mm and ${47}^{th}$ circular division coincides with main scale. Find the curved surface area of wire in true significant figures. (Given the length of wire is equal to $5.6$cm and there is no zero-error in the screw gauge)

Q. In a screw gauge, the zero of main scale coincides with fifth division of circular scale in figure (i). The circular division of screw gauge are $50$. It moves $0.5mm$ on main scale in one rotation. The diameter of the ball in figure (ii) is:

1. $2.25mm$
2. $2.20mm$
3. $1.20mm$
4. $1.25mm$

Q. To find the value of g using simple pendulum, $T=2.00s$ and $l=1.00m$ were measured. Estimate maximum permissible error in g. Also find the value of g.

Q. A student measures the time period of $100$ oscillations of a simple pendulum four times. That data set $90s,91s,95s$ and $92s$. If the minimum division in the measuring clock is $1s,$ then he reported time should be

1. $92\pm 5.0s$
2. $92\pm 2s$
3. $92\pm 3s$
4. $92=2s$

Q. A physical quantity $\rho$ is related to four variables $\alpha ,\beta ,\gamma$ and $\eta$ as $\rho =\frac{{\alpha }^3{\beta }^2}{\sqrt{\gamma \eta }}$ The percentage errors of measurements in $\alpha ,\beta ,\gamma$ and $\eta$ are 1%, 3%, 4% and 2% respectively. Find the percentage error in $\rho$.

1. 6.5%
2. 12%
3. 21%
4. 26%

Q. The circular scale of a screw gauge has 50 divisions and pitch of 0.5 mm. Find the diameter of the sphere. Main scale reading is 2.

1. 1.2 mm
2. 1.25 mm
3. 2.22 mm
4. 2.25 mm

Q. In Young’s double slit experiment, the ratio of maximum to minimum intensities of the fringe system is 4 :1. The amplitudes of the coherent sources are in the ratio:

1. $4:1$
2. $3:1$
3. $2:1$
4. $1:1$

Q. In a screw gauge, 5 complete motations of the screw cause it to a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisiors and 30 circular scale divisions. Assuming negligible zero, the thickness of the wire is:

1. $0.4300$ cm
2. $0.2150$ cm
3. $0.3150$ cm
4. $0.0430$ cm

Q. A physical quanity $P$ is releated to four observation $a,b,c$ and $d$ as follows $P=a^3{b}^3/\surd cd$The percentage errors of measurement in $a,b,c$ and $1\%,3\%,4\%$ and $2\%$ repectively. What is the percentage erros in quanity $P$? If the value of $P$. Calculated using the above relations turns out to +ve $3.763$, to what value you should round off the result?

Q. In an experiment to find zero error of vernier caliper, it is found that zero of vernier scale is left to zero of main scale and $4^{th}$ division of vernier matches with a division on main scale. Given that 9 division of main scale is equal to 10 division of vernier and one division of main scale is 1 mm. Then zero error with sign is

1. +0.4 mm
2. -0.4 mm
3. +0.6 mm
4. -0.6 mm

Q. A body travels uniformly a distance of $(13.7\pm 0.2)m$, in time $(4.0\pm 0.3)s$. The velocity of particle is ?

1. $(3.45\pm 0.31)m/s$
2. $(3.68\pm 0.4)m/s$
3. $(3.6\pm 0.42)m/s$
4. $(3.4\pm 0.3)m/s$