Tag: measurements and experimentation

Questions Related to measurements and experimentation

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

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

  1. $7\%$

  2. $9\%$

  3. $11\%$

  4. $13\%$

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Correct Option: D
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 $=13$%
Unaware about the fact that analog ammeters and voltmeters can also have zero error, a student recorded following readings while determine resistance by Ohm's law 
If the ammeter has no zero error, the zero error is the voltmeter is 
 Obs, No. Voltage/V  Current/mA   Obs No.  Voltage/V  Current/mA
 1  1.0  40  4  7.0  160
 2  3.0  80  5  9.0  200
 3  5.0  120      
physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $-1 V$

  2. $-1.5V$

  3. $0.5V$

  4. $1V$

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Correct Option: A

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

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

  1. $5\%$

  2. $4.5\%$

  3. $8\%$

  4. $7.75\%$

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Correct Option: A

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 $\left[ \alpha _ { \text { steel } } = 1.2 \times 10 ^ { - 5 \cdot 0 } C ^ { - 1 } \right]$

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

  1. $0.035 \%$

  2. $0.042 \%$

  3. $0.012 \%$

  4. $0.018 \%$

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Correct Option: B

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

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

  1. 4x

  2. $\dfrac { 1 }{ 4 } x$

  3. 2x

  4. $\dfrac { 1 }{ 2 } x$

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Correct Option: B

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  

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

  1. 59 ${ \circ } _{ C }$

  2. 8.6 ${ \circ } _{ C }$

  3. 65.56 ${ \circ } _{ C }$

  4. 58 ${ \circ } _{ C }$

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Correct Option: C

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

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

  1. $20$%

  2. $5$%

  3. $21$%

  4. $10$%

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Correct Option: A

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

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

  1. $2\%$

  2. $3\%$

  3. $1\%$

  4. $1.5$

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Correct Option: B

If the error in the measurement of radius of a sphere is 1%, then the error in the measurement of volume will be :

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

  1. 8%

  2. 5%

  3. 3%

  4. 1%

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Correct Option: C
Explanation:

We know that a sphere has volume $V=\dfrac{4}{3}\pi r^3$ meaning $V \alpha r^{3}$.
Thus, error in measurement of volume will be $ 3 \times$ 1% = 3%.

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

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

  1. $60$%

  2. $30$%

  3. $69$%

  4. $39$%

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Correct Option: A