Errors in measurement - class-XI

The main scale of a vernier callipers reads 4.7 cm, the 3 rd division on the vernier scale coincides with a main scale division while measuring the length of a rod. The least count of the vernier callipers 0.1 mm. What is the length of the rod?

A vernier having a positive zero error of +5 is used to measure the side of a 2 cm cube. The length as measure by the vernier will be : (use L.C $=$ 0.01 cm)

If the length of a vernier scale having 25 divisions corresponding to 24 main scale divisions and given that 1 MSD $=$ 1 mm, then the least count of vernier calipers is

The least count of a vernier callipers is 0.01 cm. It has an error of +0.02 cm while measuring the radius of a cylinder. The main scale reading is 3.60 cm and the 8th vernier scale division coincides with main scale, then what will be the correct radius of the cylinder?

The period of oscillation of a simple pendulum is Given by $ T=2\pi \sqrt { \frac { \ell  }{ g }  }$  where  $\ell$ is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillation is measured by a stop watch of least count 0.1 s. The percentage error in g is:-

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

If maximum percentage errors in measurement of length, mass and time are 2%,1% respectively then maximum percentage error in kinetic energy will be 

In an experiment measurements of velocity of an object $\left( {in;m{s^{ - 1}}} \right)$ are 342,33,318 and 322.The mean absolute error in the measurement is 

Measurement of two physical quantities are given as 
$x = \left( {4.0; \pm ;0.4} \right);m{s^{ - 1}}$
$Y = \left( {1.0; \pm ;0.1} \right);s$
The value of XY will be.

The maximum error in the measurement of mass and density of a cube are 3% and 1% respectively. The maximum error in the measurement of volume will be:

The time period of oscillation of simple pendulum given by $T = 2\pi\sqrt{\frac{L}{g}}$ where $L= (200 \pm 0.1) cm$. The time period, T =4s and the time of 100 oscillations is measured using a stopwatch of least count 0.1 s. The percentage error in g is

The velocity $V$ of a body starting from rest and moving with uniform acceleration a is calculated by the formula $V = \sqrt { 2 a s }$. Here $S$ represents the displacement. If error in measurement of acceleration is 4% and error in measurement of displacement is 2%, then the error in calculation of veiocity is 

The current voltage relation of diode is given by $I=\left( { e }^{ 1000V/T }-1 \right)mA$, where the applied voltage $V$ is in kelvin. If a student makes an error measuring $\pm 0.01V$ while measuring the current of $5mA$ at $300k$, what will be the error in the value of current in mA?

The heat generated in a circuit is dependent on the resistance, current and time of flow of electric current. If the percentage errors measured in the above physical quantities are 1%, 2% and 1% respectively, the maximum error in measuring the heat is :

The dimensional formula for a physical quantity $X$ is ${ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 }. $The errors in measuring the quantities $M, L$ and $T$ respectively are 2%, 3%, and 4%. The maximum percentage error that occurs in measuring the quantity $X$ is :

The percentage error in the measurement of mass and speed are 2% and 3% respectively. The maximum percentage error in the estimation of kinetic energy of a body will be:

Given $A=\dfrac{x^p}{y^qz^r}$. The percentage errors in measurement of $x, y$ and $z$ are 1 %, 0.5 % and 2% respectively. If $p=3, q=2$ and $r=1$ then the maximum percentage error in A is  

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

The kinetic energy of a particle depends on the square of speed of the particle. If error in measurement of speed of $30%$, the error in the measurement of kinetic energy will be

A physical quantity $S$ is given by $S = \dfrac {a^{2}b^{3}}{c\sqrt {d}}$.
If errors of measurements in $a, b, c, d$ are $4%, 2%, 3%, 1%$ respectively, find the percentage error in the value of $S$.

In an experiment four quantities a, b, c and d are measured with percentage error $1$ %, $2$%, $3$% and $4$% respectively. Quantity P is calculated as follows:
$P=\frac{ab^2}{\sqrt{cd^3}}$
Percentage error is P is

In a relation $ S=\dfrac{b}{b-c}$, where b, c,s are physical quantities, b is $(5.0 \pm 0.1)$ N and c is $(2.0 \pm 0.2)N$ then the percentage error in S is

The radius and height of a cone are measured as $6cms$ each by scale in which there is an error of $0.01cm$ in each cm. then the approximate error in its volume is.

In a resonant column method, resonance occurs at two successive levels of $l _1=30.7 cm$ and $l _2=63.2 cm$ using a tuning fork of $f=512 Hz$. What is the maximum error in measuring speed of sound using the relations $v=f\lambda$ and $\lambda =2(l _2-l _1)$?

Given $x=\dfrac {ab^2}{c^3}$, if the percentage errors in a, b and c are $\pm$ 1%, $\pm$ 3% and $\pm$ 2% respectively, the percentage error in $x$ can be:

The pressure on  square plate is measured by measuring the force on the plate and length of sides of plate. If the maximum error in the measurement of force and length are respectively $4$% and $2$%, the maximum error in measurement of pressure is..........

A physical quantity P is repleted to four observed a,b,c,d as follows: $P=\dfrac{a^3b^2}{\left(\sqrt c.d\right)}$ The percentage errors in the measurement of a,b,c and d are $1%3%,4%$ and $2%$ respectively. The percentage error in the quantity P is

A physical quantity $Q$ is released to four observable $x,y,z$ and $t$  by the relation
$Q=\dfrac {x^{2/5}z^{3}}{y\sqrt {t}}$ 
The percentage errors of measurement in $x,y,z$ and $t$ are $2.5%,2%,0.5%$ and $1%$ receptively. The percentage error in $Q$ will be

A steel tape is calibrated at $20 ^ { \circ } \mathrm { C }$. On a cold day when the temperature is $- 15 ^ { \circ } \mathrm { C }$ percentage error in the tape will be $\left[ \alpha _ { \text { steel } } = 1.2 \times 10 ^ { - 5 \cdot 0 } C ^ { - 1 } \right]$

The random error in the arithmetic mean of 100 observations is x, then random error in the arithmetic mean of 400 observation would be

A  faulty thermometer has its fixed point marked 5${ \circ  } _{ C }$ and 95${ \circ  } _{ C }$. this thermometer reads the temperature of a body as ${ 59 }^{ \circ  }$. The correct temperature on Celsius scale is  

If the error in measurement of momentum of a particle is $10$% and mass is known exactly,the permissible error in the determination of kinetic energy is

Length of a thin cylinder as measured by vernier callipers having least cound $0.01\ cm$ is $3.25\ cm$ and its radius of cross-section is measured by a screw gauge having least count $0.01\ mm$ as $2.75\ mm$. The percentage error in the measurement of volume of the cylinder will be

The speed of a body is measured with a positive error of 30%. If the mass of the body is known exactly, the kinetic energy is calculated with an error of

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His per-centre error in the n=measurement of g by the relation $g={ 4\pi  }^{ 2 }\left( I/T^{ 2 } \right) $ will be 

If ${ R } _{ 1 }=600\Omega \pm 1%$ and ${ R } _{ 2 }=600\Omega \pm 2%$. Find % error in the calculation of equivalent resistance when these two are connected in parallel.

A particle covers a distance of $ (13.8 \pm 0.2) \mathrm{m}  $ in$ (4 \pm 0.3)  $ seconds. Its velocity under error limits will be :-

A faulty thermometer has its fixed point marked $5C$ and $95 C$. This thermometer reads the temperature of a body as $59^o$. The correct temperature on Celsius scale is 

A resistor of $10 k\Omega$ having tolerance 10% is connected in series with another resistor of $20k\Omega$ having tolerance 20%. The tolerance of the combination will be:

What is the fractional error in g calculated from $T=2\pi \sqrt {l/g}$?

A student performs an experiment for determination of $g\left (=\dfrac {4\pi^2l}{T^2}\right )$. The error in length $l$ is $\Delta l$ and in time $T$ is $\Delta T$ and $n$ is a number of times the reading is taken. The measurement of $g$ is most accurate for :

The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively. The maximum error in measuring the heat is :

A physical quantity A is dependent on other four physical quantities p, q, r and s as given by $\displaystyle A= \frac{\sqrt{pq}}{r^{2}s^{3}}.$ The percentage error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is :

Percentage error in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and need will be

The error in the measurement of the radius of the spheres by using vernier calipers is 0.3%. The permissible error in the measurement of surface area is:

Find the percentage error in specific resistance given by $\displaystyle \rho=\frac{\pi r^{2}R}{l}$ where r is the radius having value $\displaystyle \left ( 0.2\pm 0.02 \right )$ cm, R is the resistance of $\displaystyle \left (60\pm 2 \right )\Omega $ and l is length of $\displaystyle \left ( 150\pm 0.1 \right )$ cm.

The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of the density is

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, the maximum error in the measurement of pressure is:

To estimate 'g' (from g = $4, \pi^2, \displaystyle \frac{L}{T^2}$), error in measurement of L is $\pm 2, %$ and error in measurement of T is $\pm, 3, %$. The error in estimated 'g' will be

The length, breadth and thickness of a strip are (10.0 $ \pm $ 0.1)cm, (1.00 $ \pm $ 0.01)cm and

The external and internal radius of a hollow cylinder are to be measured to be (4.23 $\pm$ 0.01)cm and (3.89 $\pm$ 0.01)cm. The thickness of the wall of the cylinder is :

The length of a cylinder is measured with a metre scale having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01cm. Given the length is 5.0 cm and diameter is 2.00cm. The percentage error in the calculated value of volume will be:

An experiment measures quantities x, y, z and then t is calculated from the data as $t, =, \displaystyle \frac{xy^2}{z^3}$. If percentage errors in x, y and z are respectively 1 %, 3 %, 2 %, then percentage error in t is

The length and breadth of a rectangular object are 25.2 cm and 16.8 cm respectively and have been measured to an accuracy of 0.1 cm. The relative error and percentage error in the area of the object are:

The percentage error in the measurement of a quantity Z which is related to two other quantities as Z = $\displaystyle x^{-1}y^{+1}$ is due to the percentage error in the measurement of x and y which are 2% and 1% respectively. Find the maximum fractional error in Z (in %).

The length of a pendulum is measured as $1.01$ m and time for $30$ oscillations is measured as $1$ minute $3$ seconds. Error in length is $0.01$ m and error in time is $3$ seconds. The percentage error in the measurement of acceleration due to gravity is:

The pressure on  a circular plate is measured by measuring force on the plate and the radius of the plate. If the errors in measurement  of the force and the radius are $5$% and $3$% respectively, the percentage of error in the measurement of pressure is:

In a measurement, the uncertainty of length $L$ is $\pm a$ and the uncertainty of width $W$ is $\pm b$. Assuming a and b very small, find the the uncertainty in measurement of area. 

In an experiment, the value of refractive index of a plastic has been found 1.33,1.30, 1.34 and 1.29 in successive measurements. Find the mean absolute error for refractive index.  

The capacitance of two capacitors are $C _1=(5 \pm 0.1)\mu F$ and $C _2=(10 \pm 0.1)\mu F$, If they are connected in series then the percentage error is 

In an experiment, mass of an object is measured by applying a known force on it, and then measuring its acceleration. If, in the experiment, the measured values of applied force and the measured acceleration are $F=10.0\pm 0.2N$ and $a=1.00\pm 0.01m/{s}^{2}$, respectively, the mass of the object is

A physical quantity $X$ is represented by $X = [M^{\eta}L^{-\theta} T^{-\phi}]$. The maximum percentage errors in the measurement of $M, L$ and $T$, respectively are $\alpha$%, $\beta$% and $\gamma$%. The maximum percentage error in the measurement of $X$ will be

The energy of a system as a function of time t is given as $E(t) = A^2 exp(- \alpha t)$, where $\alpha = 0.2 s^{-1}$. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of $E(t)$ at t = 5 s is:

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is :

The length  and width of a rectangular room are measured to be $3.95 \pm  0.05 m$ and $3.05 \pm  0.05m$, respectively. The area of the floor is 

Two resistors of resistances $R _1$ = (100 $\pm$ 3) $\Omega$ and $R _2$ = (200 $\pm$ 4) $\Omega$ are connected in parallel. The equivalent resistance of the parallel combination is:

The percentage errors in quantities $P, Q, R$ and $S$ are $0.5$%, $1$%, $3$% and $1.5$% respectively in the measurement of a physical quantity $A = \dfrac {P^{3}Q^{2}}{\sqrt {R}S}$.
The maximum percentage error in the value of $A$ will be

The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then, the maximum error in the measurement of acceleration due to gravity is:

The dimensions of a rectangular block measured with callipers having least count of 0.01 cm are 5mm x 10mm x 5 mm. The maximum percentage error in the measurement of the volume of the block is

A force $\vec { F } $ is applied on a square plate of length $L$. If the percentage error in the determination of $L$ is $3$% and in $F$ is $4$%, the permissible error in the calculation of pressure is