Tag: vernier calliper and screw gauge

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Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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 :

  1. $2\%$

  2. $3\%$

  3. $6\%$

  4. $1\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation


$ H={ I }^{ 2 }RT$ (by dimensional analysis)
$\displaystyle \frac { \triangle n }{ n } =(2\frac { \triangle I }{ I } +\frac { \triangle R }{ R } +\frac { \triangle T }{ T } )$%
          $=2(2)+1+1$
          $= 6 $ %

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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 :

  1. 19%

  2. 9%

  3. 17%

  4. 21%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ [X] = [M^{-1} L^{3} T^{-2}]$

$ \Rightarrow 
Error  = (\dfrac{\triangle M}{M} +
3 \dfrac{\triangle L}{L} + 2 \dfrac{\triangle T}{T}) %  $

$ \Rightarrow 2+3\times (3) +2\times (4)$

$\Rightarrow   $ 19  %

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The percentage errors in a, b, c are $\pm 1$%, $\pm 3$% and $\pm 2$% respectively. The percentage error in $\dfrac{a^2}{bc^3}$ is:

  1. $\pm 13$%

  2. $\pm 9$%

  3. $\pm 6$%

  4. $\pm 11$%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $Y=\dfrac { { a }^{ 2 } }{ b{ c }^{ 3 } } $
$\displaystyle \frac { \Delta Y }{ Y } \times 100=\pm \left( 2\times \frac { \Delta a }{ a } \times 100+\frac { \Delta b }{ b } \times 100+3\times \frac { \Delta c }{ c } \times 100 \right) $
                    $=\pm \left( 2\times 1+3+3\times 2 \right)$

                    $ =\pm 11$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The error in the measurement of the radius of a sphere is $0.5$ %. Find the permissible error in the measurement of surface area?

  1. $0.1$ %

  2. $10$ %

  3. $5$ %

  4. $1$ %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The percentage error in measurement of radius is given, $\dfrac{\Delta r}{r}\times 100 =0.5$%
Thus, $\dfrac{\Delta r}{r}=0.5/100=0.005$
The surface area of sphere is $S=4\pi r^2$
Take ln and differentiate, $\dfrac{\Delta S}{S}=2\dfrac{\Delta r}{r}=2\times 0.005=0.01 $
The permissible or % error in the measurement of surface area $=\dfrac{\Delta S}{S}\times 100=0.01\times 100=1$%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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:

  1. 11%

  2. 8%

  3. 5%

  4. 1%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$K.E = \dfrac{1}{2}mv^{2}$


$ \dfrac{\triangle K.E}{K.E} =

\dfrac{\triangle m}{m} + 2 \dfrac{\triangle v}{v}$

              $ = 2+2(3) = 8$%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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  

  1. $5$ %

  2. $6$ %

  3. $3$ %

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $A=\dfrac{x^p}{y^qz^r}$
Take ln and then differentiate , $\dfrac{\Delta A}{A}=\pm\left(p\dfrac{\Delta x}{x}+q\dfrac{\Delta y}{y}+r\dfrac{\Delta z}{z}\right)$
Thus the maximum percentage error in A:
$\dfrac{\Delta A}{A}\times 100=p\dfrac{\Delta x}{x}\times 100+q\dfrac{\Delta y}{y}\times 100+r\dfrac{\Delta z}{z}\times 100=(3\times 1)+(2\times 0.5)+(1\times 2)=6$ %

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The diameter of an iron rod is given by $(44.42\pm 0.03)$ mm. What does it mean?

  1. True value of diameter can be only $44.42$ mm

  2. The relative error in diameter can be $0.03 $

  3. The percentage error in diameter can be $0.03$

  4. True value of diameter can not more than $44.45$ mm and less than $44.39$ mm.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, diameter $d=44.42 $mm and $\Delta d=\pm 0.03 $mm
Thus, true value of diameter will be in between $(44.42+0.03)=44.45$ mm and$(44.42-0.03)=44.39$ mm.
The relative error $=|\dfrac{\Delta d}{d}|=\dfrac{0.03}{44.42}=6.75\times 10^{-4}$ 
The percentage error $=|\dfrac{\Delta d}{d}|\times 100=0.07 $%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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 :

  1. 9%

  2. 19%

  3. 10%

  4. 90%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ d = ML^{-3}\rightarrow  (By \   dimensional \  analysis)$


$\displaystyle \frac{\triangle d}{d} = \frac{\triangle M}{M}+ 3\frac{\triangle L}{L}$
          $ = 3+3(2)$
          $ = 9$%   

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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

  1. $30\%$

  2. $60\%$

  3. $69\%$

  4. $15\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

KE = (1/2)mv^2. If v changes by 30%, v_new = 1.3v. KE_new = (1/2)m(1.3v)^2 = 1.69 * KE_old. The percentage increase is 69%.