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Units and Measurements · Question 31

AIPMT 2015MCQEasy📈 Topic in 38% papers+4−1
1

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

Answer

(3) 1, -1, -1

Solution

[vc] = [ M0 L T-1], [ ] = [ M L-1 T-1], [ ] = [ M L-3], [r] = [L]

[ M0 L T-1] = [ M L-1 T-1]x [ M L-3]y [L]z

Comparing powers:

T: -x = -1 ⇒ x = 1

M: x + y = 0 ⇒ y = -1

L: -x - 3y + z = 1 ⇒ -1 + 3 + z = 1 ⇒ z = -1

∴ x, y, z = 1, -1, -1, i.e. vc r

Answer: (3)

AIPMT 2015

Keep practising — Units and Measurements

2

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)
3

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
4

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
5

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)
6

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)
7

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)
8

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)
9

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)
10

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

  1. e2 - e1
  2. e1 + 2e2
  3. e1 + e2
  4. e1 - 2e2
AIPMT 2010 (Mains)
11

The dimension of 12 0 E2, where 0 is permittivity of free space and E is electric field, is

  1. ML2T-2
  2. ML-1T-2
  3. ML2T-1
  4. MLT-1
AIPMT 2010 (Prelims)

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