Tag: physics

Questions Related to physics

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

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

  1. $8.5\%$

  2. $6.0\%$

  3. $7.5\%$

  4. $6.5\%$

Show answer
Correct Option: D
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 %$

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:

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

  1. $3%$

  2. $4%$

  3. $6%$

  4. $5%$

Show answer
Correct Option: D

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

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

  1. 5%

  2. 10%

  3. 15%

  4. 20%

Show answer
Correct Option: A
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.

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

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

  1. $13$%

  2. $10$%

  3. $7$%

  4. $12$%

Show answer
Correct Option: B
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$  %

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

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

  1. $-3D$

  2. $+3D$

  3. $-5D$

  4. $+5D$

Show answer
Correct Option: B

If image is real and inverted, mangification will be:

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

  1. two

  2. negative

  3. one

  4. zero

Show answer
Correct Option: B
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.

The magnification produced by a concave mirror

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

  1. is always more than one

  2. is always less than one

  3. is always equal to one

  4. may be less than or greater than one

Show answer
Correct Option: D
Explanation:

if object distance < f then m>1

else if object distance >f then m<1

The mirror used in automobiles to see the rear field of view is

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

  1. concave

  2. convex

  3. plane

  4. none of these

Show answer
Correct Option: B
Explanation:

Convex mirrors are used in automobiles to see the near field of view as convex mirror has a wider field of view and it has higher magnification.

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:

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

  1. 2.3 kg

  2. 2.34 kg

  3. 2.340 kg

  4. 2.3403 kg

Show answer
Correct Option: A
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 $= 2.3 kg$

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

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

  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 $10^{-6}m^3$

Show answer
Correct Option: A
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, $V. 1.7 \times 10^{-6} m^3$