Q91.
The determination of the value of acceleration due to gravity $(g)$ by simple pendulum method employs the formula,
$g=4\pi^2\dfrac{L}{T^2}$
The expression for the relative error in the value of $g$ is:
- $\dfrac{\Delta g}{g}=\dfrac{\Delta L}{L}+2\Big(\dfrac{\Delta T}{T}\Big)$
- $\dfrac{\Delta g}{g}=4\pi^2\Big[\dfrac{\Delta L}{L}-2\dfrac{\Delta T}{T}\Big]$
- $\dfrac{\Delta g}{g}=4\pi^2\Big[\dfrac{\Delta L}{L}+2\dfrac{\Delta T}{T}\Big]$
- $\dfrac{\Delta g}{g}=\dfrac{\Delta L}{L}-2\Big(\dfrac{\Delta T}{T}\Big)$
Explanation:
Hint: Recall error analysis.
Step: Find the expression for the relative error in .
The expression of acceleration due to gravity by simple pendulum method is given by;
The relative error in is given by;
Hence, option (1) is the correct answer.
#339775
Exam: NEET – 2022
Q92.
When the circular scale of a screw gauge completes $2$ rotations, it covers $1$ mm over the pitch scale. The total number of circular scale divisions is $50.$ The least count of the screw gauge in metres is:
- $10^{-4}$
- $10^{-5}$
- $10^{-2}$
- $10^{-3}$
Explanation:
Hint:
Step 1:
Find the pitch of the screw gauge.
The pitch of the screw gauge is given by;
Step 2: Find the least count of the screw gauge.
Hence, option (2) is the correct answer.
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Exam: NEET – 2022
Q93. The area of a rectangular field (in $\text{m}^2$ ) of length $55.3$ m and breadth $25$ m after rounding off the value, for correct significant digits is:
- $14\times10^{2}$
- $138\times10^{1}$
- $1382$
- $1382.5$
Explanation:
Hint: Apply the rules of significant figures.
Step 1: Find the area of the field.
The area of the field
Step 2: Find the result with appropriate significant figures.
The result should have as many significant figures as in the measurement given with the least significant figure.
Area = =
Hence, option (1) is the correct answer.
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Exam: NEET – 2022
Q94. The dimensions $[MLT^{-2}A^{-2}]$ belong to the:
- electric permittivity
- magnetic flux
- self-inductance
- magnetic permeability
Explanation:
Hint: The magnetic force between two current-carrying wires is given by, .
Step: Find the dimensions of each quantity.
Dimensions of electric permittivity,
Dimensions of magnetic flux,
Dimensions of self-inductance,
Dimensions of magnetic permeability,
Hence, option (4) is the correct answer.
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Exam: NEET – 2022
Q95. Plane angle and solid angle have:
- both units and dimensions
- units but no dimensions
- dimensions but no units
- no units and no dimensions
Explanation:
Hint: Plane angle and solid angle are dimensionless quantities.
Explanation: The unit of plane angle is radian while the unit of solid angle is steradian but both are dimensionless.
Hence, option (2) is the correct answer.
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Exam: NEET – 2022
Q96. The mechanical quantity, which has dimensions of reciprocal of mass $(M^{-1}),$ is:
- angular momentum
- coefficient of thermal conductivity
- torque
- gravitational constant
Explanation:
Hint: Use dimensional analysis.
Step 1: Find the dimensions of the given mechanical quantities.
(1) Angular momentum:
(2) Coefficient of thermal conductivity:
(3) Torque:
(4) Gravitational constant:
Step 2: Find The mechanical quantity, which has dimensions of reciprocal of mass.
The dimensional formula of the gravitational constant is:
Therefore, the gravitational constant has the dimensions of the reciprocal of mass .
Hence, option (4) is the correct answer.
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#368156
Exam: NEET – 2023
Q97. The diameter of a spherical bob, when measured with vernier callipers yielded the values: $3.33$ cm, $3.32$ cm, $3.34$ cm, $3.33$ cm and $3.32$ cm. The mean diameter to appropriate significant figures is:
- $3.328$ cm
- $3.3$ cm
- $3.33$ cm
- $3.32$ cm
Explanation:
Hint: .
Step 1: Find the mean diameter.
Step 2: Find the mean diameter to appropriate significant figures.
After rounding off the mean diameter to appropriate significant figures is 3.33 cm.
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Exam: NEET – 2023
Q98. The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
- Random errors
- Instrumental errors
- Personal errors
- Least count errors
Explanation:
Hint: Recall random errors.
Explanation: Random errors are those errors, unpredictable fluctuations in experimental conditions such as temperature, voltage supply, vibrations, humidity, etc., cause measurements to vary irregularly from one observation to another.
Instrumental errors are due to faulty or improperly calibrated instruments.
Personal errors are due to the observer’s mistakes (parallax, incorrect reading, etc.).
least count errors are due to the finite resolution of the measuring instrument.
Hence, option (1) is the correct answer.
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Exam: NEET – 2023
Q99. A metal wire has mass $(0.4\pm 0.002)~\text{g}$ , radius $(0.3\pm 0.001)~\text{mm}$ and length $(5\pm 0.02)~\text{cm}$ . The maximum possible percentage error in the measurement of density will nearly be:
- $1.4 \%$
- $1.2 \%$
- $1.3 \%$
- $1.6 \%$
Explanation:
Hint: Use the concept of relative error.
Step 1: Find the expression for the density of the wire.
The density of the wire is given by;
Step 2: Find the maximum possible percentage error in the density of the wire.
Hence, option (4) is the correct answer.
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Exam: NEET – 2023
Q100. The potential energy of a particle moving along the $x\text-$ direction varies as ${V}=\dfrac{{A}x^{2}}{\sqrt{x}+{B}}.$ The dimensions of $\dfrac{A^2}{B}$ are:
- $[{M}^{3/2}{L}^{1/2}{T}^{-3}]$
- $[M^{1/2}LT^{-3}]$
- $[{M}^2{L}^{1/2}{T}^{-4}]$
- $[ML^{2}T^{-4}]$
Explanation:
Hint:
Step: Find the dimensions of
Given:
According to the principle of homogeneity, only the physical quantities having the same dimensional formula only can be added or subtracted.
Hence, option (3) is the correct answer.
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Exam: NEET – 2024
