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Units and Measurements · Question 29

NEET 2017MCQMedium📈 Topic in 38% papers+4−1
1

A physical quantity of the dimensions of length that can be formed out of c, G and e24 0 is [c is velocity of light, G is the universal constant of gravitation and e is charge]

  1. c2 [G e24 0 ]1/2
  2. 1c2 [ e2G 4 0 ]1/2
  3. 1cG e24 0
  4. 1c2 [G e24 0 ]1/2

Answer

(4) 1c2 [G e24 0 ]1/2

Solution

[ e24 0 ] = [F r2] = [ML3T-2], [G] = [M-1L3T-2], [c] = [LT-1]

Let L = cx Gy ( e24 0 )z

[L] = [LT-1]x [M-1L3T-2]y [ML3T-2]z

M: -y + z = 0; L: x + 3y + 3z = 1; T: -x - 2y - 2z = 0

y = z, x = -4y

-4y + 6y = 1 y = z = 12, x = -2

Length = 1c2 [G e24 0 ]1/2

Answer: (4)

NEET 2017

Keep practising — Units and Measurements

2

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ?

  1. hGc3/2
  2. hGc5/2
  3. hcG
  4. Gch3/2
NEET 2016 (Phase 2)
3

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ x y rz] where , 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

  1. -1, -1, -1
  2. 1, 1, 1
  3. 1, -1, -1
  4. -1, -1, 1
AIPMT 2015
4

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

  1. [EV-2T-2]
  2. [E-2V-1T-3]
  3. [EV-2T-1]
  4. [EV-1T-2]
AIPMT 2015 (Cancelled)
5

If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions of mass are

  1. [FVT-1]
  2. [FVT-2]
  3. [FV-1T-1]
  4. [FV-1T]
AIPMT 2014
6

In 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 = a3 b2cd. % error in P is

  1. 7%
  2. 4%
  3. 14%
  4. 10%
NEET 2013
7

The pair of quantities having same dimensions is

  1. Impulse and Surface Tension
  2. Angular momentum and Work
  3. Work and Torque
  4. Young's modulus and Energy
NEET 2013 (Karnataka)
8

The dimensions of ( 0 0)-1/2 are

  1. [ L1/2T-1/2]
  2. [ L-1T]
  3. [ LT-1]
  4. [ L1/2T1/2]
AIPMT 2012 (Mains)
9

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

  1. kg m s-1
  2. kg m s-2
  3. kg s-1
  4. kg s
AIPMT 2012 (Prelims)
10

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

  1. 0.04
  2. 0.4
  3. 40
  4. 400
AIPMT 2011 (Mains)
11

The dimensions of ( 0 0)-1/2 are

  1. [ L1/2T-1/2]
  2. [ L-1T]
  3. [ LT-1]
  4. [ L1/2T1/2]
AIPMT 2011 (Prelims)

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