Tag: least count of vernier calliper and screw gauge

Questions Related to least count of vernier calliper and screw gauge

The main scale of a vernier callipers reads 4.7 cm, the 3 rd division on the vernier scale coincides with a main scale division while measuring the length of a rod. The least count of the vernier callipers 0.1 mm. What is the length of the rod?

  1. 4.62 cm

  2. 4.61 cm

  3. 4.72 cm

  4. 4.73 cm


Correct Option: D
Explanation:

$LC = 0.01 mm = 0.01 cm$
Length of the rod $=$ MSR + (VCD $\times$ LC)
$=4.7 cm + (3 \times 0.01)$
$=(4.7 + 0.03) cm$
$=4.73  cm$

A vernier having a positive zero error of +5 is used to measure the side of a 2 cm cube. The length as measure by the vernier will be : (use L.C $=$ 0.01 cm)

  1. 1.95 cm

  2. 2 cm

  3. 2.05 cm

  4. Cannot say


Correct Option: C
Explanation:

Correction $=-0.505 cm (-5 \times 0.01 cm)$
Corrected reading $=$ Observed reading + correction
2 $=$ Observed reading + (-0.05) cm.
Observed reading $=$ 2.05 cm

If the length of a vernier scale having 25 divisions corresponding to 24 main scale divisions and given that 1 MSD $=$ 1 mm, then the least count of vernier calipers is

  1. 0.004 cm

  2. 4 micrometer

  3. 0.04 mm

  4. 0.04 m


Correct Option: A,C
Explanation:

Given
N $=$ 25
25 VSD $=$ 24 MSD
1 MSD $=$ 1mm
$\therefore LC \displaystyle = \frac{MSD}{No.   of   VSD} = \frac{1mm}{25}$
$=0.04 mm$
$=0.04 \times 10^{-1} cm$
$=0.004 cm$
$=0.004 \times 10^{-2} m$
$=40  \mu m$

A vernier has a negative zero error. When the jaws $J _1$ and $J _2$ are brought in contact the zero of the vernier must :

  1. Coincide with the zero of the main scale.

  2. Be to the right of the zero of the main scale.

  3. Be to the left of the zero of the main scale.

  4. None of the above.


Correct Option: C
Explanation:

A vernier caliper is said to have a negative zero error when the zero of the vernier lies to left to the zero of the main scale if both the jaws are brought together.

In vernier callipers, if $L.C = l$ and pitch is P then $\displaystyle \frac{l}{P}$ is :

  1. Always less than 1

  2. Always greater than 1

  3. Equal to 1

  4. None of these


Correct Option: A
Explanation:

L.C $=$ 0.1 mm $=l$
pitch $=1$ mm  $=$ p
$\displaystyle \frac{l}{p} = \frac{0.1}{1} = 0.1  <  1$

The least count of a vernier callipers is 0.01 cm. It has an error of +0.02 cm while measuring the radius of a cylinder. The main scale reading is 3.60 cm and the 8th vernier scale division coincides with main scale, then what will be the correct radius of the cylinder?

  1. 1.72

  2. 1.75

  3. 1.83

  4. 1.87


Correct Option: C
Explanation:

L.C. $=$ 0.01 cm
Error $=$ + 0.02 cm $\Rightarrow$ Positive zero
error $=$ + 0.02 cm
main scale reading (MSR) $=$ 3.60 cm 8$^{th}$ vernier scale coincides with main scale
$\Rightarrow$ vernier coincidence (VC) $=$ 8
We know that
Correct diameter $=$ [main scale reading+ (L.C $\times$ V.C)] - (error)
$=$ [3.60 + (0.01 $\times$ 8)] - [+ 0.002]
$=$ (3.60 + 0.08)- (+0.02)
$=$ 3.68 - 0.02
$=$ 3.66 cm
$\therefore correct radius = \displaystyle \frac{diameter}{2} = \frac{3.66}{2}$
$=1.83 cm$

A liquid of low specific heat capacity is preferred as a thermometric liquid.

  1. True

  2. False

  3. Either

  4. Neither


Correct Option: A

The period of oscillation of a simple pendulum is Given by $ T=2\pi \sqrt { \frac { \ell  }{ g }  }$  where  $\ell$ is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillation is measured by a stop watch of least count 0.1 s. The percentage error in g is:-

  1. 0.1 %

  2. 1 %

  3. 0.2 %

  4. 0.8 %


Correct Option: C

In an experimental set up, the density of a small sphere is to be determined. The diameter of the small sphere is measured with the help of a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the sphere has a relative error of 2%, the relative percentage error in the density is

  1. $0.03$%

  2. $3.11$%

  3. $0.08$%

  4. $8.2$%


Correct Option: A

A shpere has a mass of 12.2 kg $\pm $ 0.1 kg and radius 10 cm $\pm $ 0.1 cm, h=the maximum % error in density is 

  1. 10%

  2. 2.4%

  3. 3.83%

  4. 4.2%


Correct Option: C