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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$  %

Multiple choice physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

A convex lens of 2 D power is joined with a concave mirror of 1 D power. Equivalent power of instrument will be

  1. $-3D$

  2. $+3D$

  3. $-5D$

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

The power of a lens is P = 1/f. When a lens and a mirror are combined, the equivalent power is P_eq = P_lens + P_mirror. Given P_lens = +2D and P_mirror = +1D, the total power is +3D.

Multiple choice physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

If image is real and inverted, mangification will be:

  1. two

  2. negative

  3. one

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

According to new Cartesian sign convention, image size for erect image is considered positive and that of inverted image is considered negative.

The object being always erect, the object size is always positive.
So, magnification for a real image, being a ratio of image size and object size is considered negative.

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is:

  1. 2.3 kg

  2. 2.34 kg

  3. 2.340 kg

  4. 2.3403 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, mass of the box, $m = 2.3 kg$
Mass of one gold piece, $m _1 = 20.15 g = 0.02015 kg$
Mass of other gold piece, $m _2 = 20.17 g = 0.02017 kg$
$\therefore$ Total mass = $m + m _1 +m _2 = 2.3 kg + 0.02015 kg +0.02017 kg = 2.34032 kg$
As the result is correct only upto one place of decimal, therefore, on rounding off, we get Total mass $= 2.3 kg$

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

A cube has a side of length 1.2 x $10^{-2}$. Its volume upto correct significant figures is

  1. 1.7 x $10^{-6}m^3$

  2. 1.73 x $10^{-6}m^3$

  3. 1.78 x $10^{-6}m^3$

  4. 1.732 x $10^{-6}m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Here
Length of the cube, $L =12 x10^{-2} m$
Volume of the cube, $V= (1.2 \times10^{-2} m)^3= 1.728 \times 10^{-6}m^3$
As the result can have only two significant figures, therefore, on rounding off, we get, $V. 1.7 \times 10^{-6} m^3$