Unit ans Measurement NEET

 
NEET 2022 

Question 1. The percentage error in the measurement of g is : (Given that `g={4\pi^2L}/{T^2}`, `L=(10\pm0.1)cm, T=(100\pm1)s`
g के मापन में प्रतिशत त्रुटि है: (दिया गया है कि `g={4\pi^2L}/{T^2}`, `L=(10\pm0.1)cm, T=(100\pm1)s`

(a) `7%`
(b) `2%`
(c) `5%`
(d) `3%`

Answer (d)


Question 2. The dimensions `[MLT^-2A^-2]` belong to the

(a) Magnetic Flux
(b) Self inductance
(c) Magnetic Permebility
(d) Electric Permittivity

Answer (c)


Question 3,.Plane angle and solid angle have

(a) Units but no dimensions
(b) Dimensions but no units
(c) No units and no dimensions
(d) Both units and dimensions

Answer (a)


Question 4. The area of a rectangular field (in `m^2`) of length `55.3 m` and breadth `25 m` after rounding off the value for correct significant digits is

(a) `138\times10^1`
(b) `1382`
(c) `1382.5`
(d) `14\times10^2`

Answer (d)


NEET 2021

Question 5. The E and G respectively denote energy and gravitational constant, then `E/G` has the dimensions of :

(a) `[M^2] [L^-2] [T^-1]`
(b) `[M^2] [L^-1] [T^0]` 
(c) `[M] [L^-1][T^-1]`
(d) `[M] [L^0] [T^0]`

Answer (b)

Question 6. A screw gauge gives the following readings when used to measure the diameter of a wire

Main scale reading : `0 mm`

Circular scale reading : `52` divisions

Given that 1 mm on main scale corresponds to `100` divisions on the circular scale. The diameter of the wire from the above data is :

(a) `0.052cm`
(b) `0.52cm`
(c) `0.026cm`
(d) `0.26cm`

Answer (a)


Question 7. If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

(a) `[F][A^-1][T]`
(b) `[F][A][T]`
(c) `[F][A][T^2]`
(d) `[F][A][T^-1]`

Answer (c)

Question 8. A screw gauge has least count of `0.01 mm` and there are `50` divisions in its circular scale.

The pitch of the screw gauge is :

(a) `0.25mm`
(b) `0.5mm`
(c) `1.0mm`
(d) `0.01mm`

Answer (b)

NEET 2020

Question 9. Taking into account of the significant figures, what is the value of `9.99m-0.0099m?`
महत्वपूर्ण आंकड़ों को ध्यान में रखते हुए, का मूल्य क्या है `9.99m-0.0099m?`

(a) `9.98m`
(b) `9.980m`
(c) `9.9m`
(d) `9.9801m`

Answer (a)

Question 10. Dimensions of stress are :

(a) `[ML^2T^-2]`
(b) `[ML^0T^-2]`
(c) `[ML^-1T^-2]`
(d) `[MLT^-2]`

Answer (c)

Question 11. The energy required to break one bond in DNA is `10^{-20} J`. This value in eV is nearly :
DNA में एक बंधन को तोड़ने के लिए आवश्यक ऊर्जा `10^{-20} J` है। eV में यह मान लगभग है:

(a) `0.6`
(b) `0.06`
(c) `0.006`
(d) `6`

Answer (b)

NEET 2019

Question 12. In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are `1%, 2 %, 3 %`and `4 %` respectively. Then the maximum percentage of error in the measurement `X`, where `X ={A^2B^{1/2}}/{C^{1/3}D3}` , will be :
एक प्रयोग में, भौतिक राशियों A, B, C और D के मापन में त्रुटि का प्रतिशत क्रमशः `1%, 2%, 3%` और `4%` है। फिर माप `X` में त्रुटि का अधिकतम प्रतिशत, जहाँ
 `X ={A^2B^{1/2}}/{C^{1/3}D3}`, होगा :

(a) `16%`
(b) `-10%`
(c) `10%`
(d) `(3/{13})%`

Answer (a)

NEET 2018

Question 13. A student measured the diameter of a small steel ball using a screw gauge of least count `0.001 cm`. The main scale reading is `5 mm` and zero of circular scale division coincides with `25` divisions above the reference level. If screw gauge has a zero error of `–0.004 cm`, the correct diameter of the ball is

एक छात्र ने `0.001` सेमी अल्पतमांक वाले स्क्रूगेज का उपयोग करके स्टील की एक छोटी गेंद का व्यास मापा। मुख्य स्केल रीडिंग `5` मिमी है और सर्कुलर स्केल डिवीजन का शून्य संदर्भ स्तर से ऊपर `25` डिवीजनों के साथ मेल खाता है। यदि स्क्रू गेज में `-0.004` सेमी की शून्य त्रुटि है, तो गेंद का सही व्यास है

(a) `0.521cm`
(b) `0.525cm`
(c) `0.053cm`
(d) `0.529cm`

Answer (d)


NEET 2017

Question 14. A physical quantity of the dimensions of length that can be formed out of c, G and `{e^2}/{4\pi\varepsilon_0}` is [c is velocity of light, G is the universal constant of gravitation and e is charge]

लंबाई के आयामों की एक भौतिक मात्रा जिसे c, G और से बनाया जा सकता है`{e^2}/{4\pi\varepsilon_0}` है [c प्रकाश का वेग है, G गुरुत्वाकर्षण का सार्वभौमिक स्थिरांक है और e आवेश है]

(a) `C^2[G-{e^2}/{4\pi\varepsilon_0}]^\frac{1}{2}`

(b) `1/C^2[{e^2}/{G4\pi\varepsilon_0}]^\frac{1}{2}`

(c) `1/C G{e^2}/{4\pi\varepsilon_0}`

(d) `1/C^2 [ G{e^2}/{4\pi\varepsilon_0}]^\frac{1}{2}`

Answer (d)

NEET 2016

Question 15. Planck's constant (h), speed of light in vacuum (c) and Newton's gravitional constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ?
प्लैंक का स्थिरांक (h), निर्वात में प्रकाश की गति (c) और न्यूटन का गुरुत्वाकर्षण स्थिरांक (G) तीन मूलभूत स्थिरांक हैं। इनमें से किस संयोजन में लंबाई का आयाम है?

(a) `\frac{\sqrt{hG}}{c^\frac{3}{2}}`
(b) `\frac{\sqrt{hG}}{c^\frac{5}{2}}`
(c) `\sqrt{\frac{hc}{G}}`
(d) `\sqrt{\frac{Gc}{h^\frac{3}{2}}}`

Answer (a)


AIPMT 2015

Question 16. If dimensions of critical velocity `u_c` of a liquid flowing through a tube are expressed as `[\eta^x \rho^y r^z]` where `\eta, \rho`  and `r` are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of `x`, `y` and `z` are given by

दि महत्वपूर्ण वेग के आयाम `u` एक ट्यूब के माध्यम से बहने वाले तरल के सी के रूप में व्यक्त किया जाता है  `[\eta^x \rho^y r^z]` कहाँ `\eta, \rho` और `r` क्रमशः द्रव की श्यानता, द्रव का घनत्व और ट्यूब की त्रिज्या का गुणांक है, तो `x, y` और `z` के मान इस प्रकार दिए जाते हैं

(a) `-1, -1, -1`
(b) `1, 1, 1,`
(c) `1, -1, -1`
(d) `-1, -1, 1`

Answer (c)


Question 17. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
यदि ऊर्जा (E), वेग (V) और समय (T) को मौलिक मात्रा के रूप में चुना जाता है, तो पृष्ठ तनाव का विमीय सूत्र होगा

(a) `[EV^-2T^-2]`
(b) `[E^-2V^-1T^-3]`
(c) `[EV^-2T^-1]`
(d) `[EV^-1T^-2]`

Answer (a)

AIPMT 2014

Question 18.  If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions of mass are
यदि बल (F), वेग (V) और समय (T) को मौलिक इकाइयों के रूप में लिया जाए, तो द्रव्यमान के आयाम हैं

(a) `[FVT^-1]`
(b) `[FVT^-2]`
(c) `[FV^-1T^-1]`
(d) `[FV^-1T]`

Answer (d)

NEET 2013

Question 19. The pair of quantities having same dimensions is
समान विमाओं वाली राशियों का युग्म है

(a) Impulse and Surface Tension

(b) Angular momentum and Work

(c) Work and Torque

(d) Young's modulus and Energy

Answer (c)


Question 20. If an experiment four quantities `a, b, c` and `d` are measured with percentage error `1%, 2%, 3%` and `4%` respectively.

Quantity P is calculated as follows `P = \frac{a^3b^2}{cd}%` error in `P` is

(a) `7%`
(b) `4%`
(c) `14%`
(d) `10%`

Answer (c)

AIPMT 2012

Question 21. The dimensions of `(\mu_0\varepsilon_0)^\frac{-1}{2}` are

(a) `[L^\frac{1}{2} T^\frac{-1}{2}]`

(b) `[L^-1T]`

(c) `[LT^-1]`

(d) `[L^\frac{1}{2} T^\frac{1}{2}]`

Answer (c)

Question 22. The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

(a) `kgms^-1`
(b) `kgms^-2`
(c) `kgs^-1`
(d) `kgs`

Answer (c)


AIPMT 2011

Question 23. The density of a material in `CGS` system of units is `4 g cm^-3`. In a system of units in which unit of length is `10 cm` and unit of mass is `100 g`, the value of density of material will be

(a) `0.04`
(b) `0.4`
(c) `40`
(d) `400`

Answer (c)

Question 24. The dimensions of `(\mu_0\varepsilon_0)^\frac{-1}{2}` are

(a) `[L^\frac{1}{2} T^\frac{-1}{2}]`

(b) `[L^-1T]`

(c) `[LT^-1]`

(d) `[L^\frac{1}{2} T^\frac{1}{2}]`

Answer (c)

AIPMT 2010 

Question 25. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is

(a) `e_2-e_1`
(b) `e_1+2e_2`
(c) `e_2+e_1`
(d) `e_1-2e_2`

Answer (b)

Question 26. The dimension of `\frac{1}{2}\varepsilon_0E^2`, where `\varepsilon_0` is permittivity of free space and E is electric field, is

(a) `ML^2T^-2`
(b) `ML^-1T^-2`
(c) `ML^2T^-1`
(d) `MLT^-1`

Answer (b)


AIPMT 2009

Question 27. If the dimensions of a physical quantity are given by `M^a L^b T^c`, then the physical quantity will be

(a) Velocity if `a=1, b=0, c=-1`
(b) Acceleration if `a=1, b=1, c=-2`
(c) Force if `a=0, b=-1, c=-2`
(d) Pressure if `a=1, b=-1, c=-2`

Answer (d)

AIPMT 2008

Question 28. If the error in the measurement of radius of a sphere is `2%`, then the error in the determination of volume of the sphere will be

(a) `8%`
(b) `2%`
(c) `4%`
(d) `6%`

Answer (d)

Question 29. Which two of the following five physical parameters have the same dimensions?

1.  Energy density

2.  Refractive index

3.  Dielectric constant

4.  Young's modulus

5.  Magnetic field

(a) `1&4`
(b) `1&5`
(c) `2&4`
(d) `3&5`

Answer (a)

AIPMT 2007

Question 30. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

(a) `[ML^2T^-2]`
(b) `[ML^2T^-1I^-1]`
(c) `[ML^2T^-3I^-2]`
(d) `[ML^2T^-3I^-1]`

Answer (c)

AIPMT 2006

Question 31. The velocity v of a particle at time t is given by `v = at +\frac{b}{t+c}` , where a, b and c are constants. The dimensions of a, b and c are

(a) `[L],[LT]and [LT^-2]`
(b) `[LT^-2],[L] and [T]`
(c) `[L^2],[T] and [LT^-2]`
(d) `[LT^-2], and [LT] and [L]`

Answer (b)

AIPMT 2005

Question 32. The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of

(a) Times
(b) Frequency
(c) Angular momentum
(d) Velocity

Answer (b)

AIPMT 2004

Question 33. The dimensions of universal gravitational constant are

(a) `[M^-1L^3T^-2]`
(b) `[ML^2T^-1]`
(c) `[M^-2L^3T^-2]`
(d) `[M^-2L^2T^-1]`

Answer (a)

Question 34. The unit of permittyvity of free space, `\varepsilon_0`, is

(a) `C/{N-m}`

(b) `{N-m^2}/C^2`

(c) `C^2/{N-m^2}`

(d) `C^2/{(N-m)^2}`

Answer (c)

AIPMT 2001

Question 35. The dimensions of Planck's constant equals to that of

(a) energy
(b) momentum
(c) angular momentum
(d) power

Answer (c)

AIPMT 2000

Question 36. Which pair do not have equal dimensions ?

(a) Energy and torque
(b) Force and impulse
(c) Angular momentum and Plank constant
(d) Elastic modulus and Pressure

Answer (b)