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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

If $x=10.0 \pm 0.1$ and $y=10.0 \pm 0.1$, then $2x-2y$ is equal to

  1. $(0.0 \pm 0.1)$

  2. $Zero$

  3. $(0.0 \pm 0.4)$

  4. $(20 \pm 0.2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Apply formula

$(A\pm \Delta A)-(B\pm \Delta B)=(A-B)\pm (\Delta A-\Delta B)$

Similarly

  $ 2x-2y=2\left( 10.0\pm 0.1 \right)-2\left( 10\pm 0.1 \right) $

 $ =\left( 2\times 10-2\times 10 \right)\pm (2\times 0.1-2\times 0.1) $

 $ =0 $

Hence, $2x-2y=ZERO$ 

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

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 $S$.

  1. <span>$7.5\%$.</span>

  2. <span>$17.5\%$.</span>

  3. <span>$27.5\%$.</span>

  4. <span>$10.5\%$.</span>
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

S = (a^2 * b^3) / (c * d^0.5). dS/S = 2*da/a + 3*db/b + dc/c + 0.5*dd/d. dS/S = 2(4%) + 3(2%) + 3% + 0.5(1%) = 8% + 6% + 3% + 0.5% = 17.5%.

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

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

  1. $4$%

  2. $7$%

  3. $9$%

  4. $10$%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Quantity $P$ is calculated as follow $P = \frac{{a{b^2}}}{{\sqrt {c{d^3}} }}$

Formula of % error should be,
% error in $P=3 \times$%error in $a+2 \times $% error in $b+$%error in $c+$% error in d
Given,
% error in $a=1$%
% error in $b=2$%
% error in $c=3$%
% error in $d=4$%
Hence,
% error in $P=3 \times 1+2 \times 2+3+4$
$=3$%-$4$%+$3$%+$4$%
$=10$%
$\therefore $ Option $D$ is correct answer.

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

The radius of a sphere is measured as  $ (10 \pm 0.02) $ cm. The error in the measurement of its volume is:

  1. 251 cc

  2. 25.1cc

  3. 2.51 cc

  4. 251.2cc
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that,

$r = 10$

$\Delta r=0.02$


 We know that,

The volume of sphere is

  $ V=\dfrac{4}{3}\pi {{r}^{3}} $

 $ V=\dfrac{4}{3}\times 3.14\times {{\left( 10 \right)}^{3}} $

 $ V=4186.7\,cc $

Now, taking log

$\log V=\log \dfrac{4}{3}+3\log r$

Differentiating on both sides

$\dfrac{\Delta V}{V}=0+3\dfrac{\Delta r}{r}$

Now, the error is

  $ \dfrac{\Delta V}{V}=3\times \dfrac{\Delta r}{r} $

 $ \Delta V=V\times 3\times \dfrac{\Delta r}{r} $

 $ \Delta V=4186.7\times 3\times \dfrac{0.02}{10} $

 $ \Delta V=25.1\,cc $

Hence, the error in the measurement of its volume is $25.1$ cc

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

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.

  1. $.14$

  2. $.12$

  3. $.36$

  4. $0.16$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Formula,

$V=\pi r^2 \dfrac{h}{3}$

$=\pi\times 6^2 \dfrac{6}{3}=226.19$

$\dfrac{\Delta V}{V}=\dfrac{\pi}{3}6 \times 0.01 \times 0.01=0.000628$

The change in volume is,

$V=0.000628\times 226.19=0.14$%

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

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 $\lambda =2(l _2-l _1)$?

  1. 256 cm/sec

  2. 92 cm/sec

  3. 128 cm/sec

  4. 102.4 cm/sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The maximum error is given by :


$c=f\lambda = 512 \times 2(l _2-l _1)=512 \times 2 \times (63.2-30.7) = 332.8 \ m/s$

$\dfrac{\Delta c}{c} = \dfrac{\Delta {f}}{f}  + \dfrac{ {\Delta \lambda}}{\lambda}$

Least count of scale $=0.1 cm$ 

total error in measurement of $\lambda$ 

$\Rightarrow 2\times L.C. =0.2 cm$

Total error in measurement of $f$  $\Rightarrow 0$

$\dfrac{\Delta c}{332.8} = \dfrac{0}{f}  + \dfrac{ {0 .2}}{65}$

$\Delta c =  \dfrac{ {0.2}}{65}\times 332.8 =1.024 \ m/s =102.4 \ cm/s$

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

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:

  1. $\pm$ 13%

  2. $\pm$ 7%

  3. $\pm$ 18%

  4. $\pm$ 19%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The given quantity is   $x = \dfrac{ab^2}{c^3}$
Maximum percentage error in $x$ is   $\dfrac{\Delta x}{x}\times 100 = [\dfrac{\Delta a}{a}+2\dfrac{\Delta b}{b}+3\dfrac{\Delta c}{c}]\times 100$
$\dfrac{\Delta x}{x}\times 100 = [1+2\times 3+3\times 2] = \pm 13$ %

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

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..........

  1. 1%

  2. 2%

  3. 6%

  4. 8%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pressure P = Force / Area = F / L^2. dP/P = dF/F + 2*dL/L. dP/P = 4% + 2(2%) = 4% + 4% = 8%.

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

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

  1. $7\%$

  2. $9\%$

  3. $11\%$

  4. $13\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$P=\dfrac { { a }^{ 3 }{ b }^{ 2 } }{ \sqrt { cd }  } $

$\dfrac { \Delta P }{ P } =\dfrac { 3\Delta a }{ a } +\dfrac { 2\Delta b }{ b } +\dfrac { 1 }{ 2 } \dfrac { \Delta c }{ c } +\dfrac { \Delta d }{ d } $

$\left( \dfrac { \Delta P }{ P } \times 100 \right) $% $=\left( 3\times \dfrac { \Delta a }{ a } \times 100+2\times \dfrac { \Delta b }{ b } \times 100+\dfrac { 1 }{ 2 } \times \dfrac { \Delta c }{ c } \times 100+\dfrac { \Delta d }{ d } \times 100 \right) $%
                              $=3\times 1+2\times 3+\dfrac { 1 }{ 2 } \times 4+2$
                              $=3+6+2+2=13$%
Percentage error $=13$%