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 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

  1. $8.5\%$

  2. $6.0\%$

  3. $7.5\%$

  4. $6.5\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Percentage error $\dfrac{\Delta A}{A} \times 100 = 3 \dfrac{\Delta P}{P} \times 100 + 2 \dfrac{\Delta Q}{Q} + \dfrac{1}{2} \dfrac{\Delta R}{R} \times 100 + \dfrac{\Delta S}{S} \times 100$ 

$ = 3 \times 0.5 + 2 \times 1+ 0.5 \times 3 + 1.5 = 6.5 %$

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 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:

  1. $3%$

  2. $4%$

  3. $6%$

  4. $5%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

g = 4 * pi^2 * L / T^2. Relative error dg/g = dL/L + 2 * dT/T. Given dL/L = 1% and dT/T = 2%, dg/g = 1% + 2 * 2% = 5%.

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

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

  1. 5%

  2. 10%

  3. 15%

  4. 20%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given :  $l = 10 \ mm = 1 \ cm$     $b = 5 \ mm = 0.5 \ cm$        $h = 5 \ mm  = 0.5 \ cm$
Error in the measurements   $\Delta l = \Delta b = \Delta h = 0.01 \ cm$
Maximum percentage error in volume   $\dfrac{\Delta V}{V}\times 100 = \dfrac{\Delta l}{l}\times 100 +\dfrac{\Delta b}{b}\times 100+\dfrac{\Delta h}{h}\times 100$
$\implies \ \dfrac{\Delta V}{V}\times 100 = \dfrac{0.01}{1}\times 100+\dfrac{0.01}{0.5}\times 100+\dfrac{0.01}{0.5}\times 100 = 5$ %
Correct answer is option A.
Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

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

  1. $13$%

  2. $10$%

  3. $7$%

  4. $12$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pressure  $P=\cfrac { F }{ A } =\cfrac { F }{ { L }^{ 2 } } $
Percentage error in pressure  $\cfrac { \Delta P }{ P } \times 100=\cfrac { \Delta F }{ F } \times 100+2\cfrac { \Delta L }{ L } \times 100$
$ = 4+2\times 3 = 10$  %