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In an experiment the percentage of error occured 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 = \frac{A^2 B ^{1/2 }}{C^{1/2 }D^3}  will be : 

 

  • Option 1)

    (3/13) % 

  • Option 2)

    16 % 

  • Option 3)

    - 10 % 

  • Option 4)

    10 % 

Option 1)(3/13) % Option 2)16 % Option 3)- 10 % Option 4)10 % 

(1)  

It is scalar quantity

(2)  

Value of mass not depends on gravity

(3)  

mass of a body is given by m=\frac{m_o}{\left (1-\frac{v^2}{c^2} \right )}, here symbol have their usual meaning.

(4)  

mass can never be zero.

Option (3) is correct.  Because the "" here is relativistic mass and  is rest mass.This equation tells about the relativistic mass change when an object travels at a very high speed. Hence this is incorrect about the mass.  Also mass is a scalar quantity and it can not be zero, because according to law f conservation od mass, Mass can neither be created nor destroyed.

10esu=?dyn

esu is the unit of Charge whereas dyne is the unit of Force
How to determine the formula if physical quantities are given
For this we should know the dependence of the physical quantity on other quantities and consider it as a product type of the dependence. Q)Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to...

A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e^{2}}{4\pi \varepsilon _{o}} is (c is velocity of light, G is universal constant of gravitation and e is charge)  

To solve these questions first write dimentions of all the given quantity in term of fundamental quantity and then find relation between them. - wherein     on comparing both sides we get
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is : a) 6% b) 2.5% c) 3.5% d) 4.5%
density = mass/volume volume=l^3 if side is l =1.5+3=4.5%
Opera_Snapshot_2019-02-28_095718_www.entrance360.com.png The physical quantities not having same dimensions are a) torque and work c) stress and Young's modulus Correct Option momentum and Planck's constant

c) youngs modulus = stress/strain

strain is dimensioless

so dimension of stress= dimension of youngs modulus

Opera_Snapshot_2019-02-28_102013_www.entrance360.com.png A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C In(BD) holds true Then which of the combination is not a meaningful quantity ?
the term inside the log should be dimensionless, so BD is dimensionless so dimension of [B]=1/[D] and [AD]=[C] So dimension of [A] is not equal to [C], so we cannot subtract A and C
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
@ A Harshika Sri Surface Tension = Surface Tension = 

The dimension of \left ( \mu_{\text{o}}\in_{\text{o}} \right )^{-\frac{1}{2}} are :

  • Option 1)

    \left [ \text{L}^{-\frac{1}{2}}\text{T}^{\frac{1}{2}} \right ]

  • Option 2)

    \left [ \text{L}^{\frac{1}{2}}\text{T-}^{\frac{1}{2}}\right ]

  • Option 3)

    \left [ \text{L}^{-1}\text{T}\right ]

  • Option 4)

    \left [ \text{LT}^{-1}\right ]

 
Option 1) Option 2) Option 3) Option 4)
That error in parallel resistance part is what I m not getting....How is it derived?
@ Anupam  Since R1 and R2 are in parallel  So  Differtiate LHS we get                                                                            Similary We get for RHS                                                                                             &                                       So from equation 1,2 ,3 4 We get                                                              ...
ec.PNG For two masses m1 and m2  following measurment are taken  m1=28.7+0.5 kg m2=19.6+03 kg What is the percentage error in  M=m1+m2
  @Sushant Hajare ec.PNG ec.PNG
For a measurment of a length of cylinder by vernier callipers following reading are taken 3.29 cm 3.28 cm 3.29 cm 3.31 cm 3.28 cm 3.27 cm 3..29cm 3.30 cm Absolute error in measurement is -
@Sushant Hajare
In the measurment of the period of a simple pendulum the readings turn out to be (1) 2.63 s (2) 2.56 s (3) 2.42 s (4) 2.71 s (5) 2.80 s Calculate % error in the measurment -->
@Sushant Hajare  The mean period of oscillation will be  T=2.63+2.56+2.42+2.71+2.8/5 =2.62 sec The errors in the measurement wil be  2.63-2.62=.01sec 2.56-2.62=-.06sec 2.42-2.62=-.2sec 2.71-2.62=.09sec 2.80-2.62=.18 sec so mean of absolute error will be .11sec Hence Period of oscillation will be (2.62±0.11) Therefore T=2.6±.1s relative error or percentage error is given...
1 calorie = 4.2 J , where But in a new system unit of mass equals to Kg . The unit of length m and the unit of time Sec . Then 1 calorie has a magnitude of
@Sushant Hajare 1 calorie = 4.2 J , where But in a new system unit of mass equals to Kg, the unit of length m and the unit of time Sec . Then 1 calorie has a magnitude of Answer:      
The density of material in CGS system of units is 4g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be
@Sushant Density in CGS system is =  4  gms/ cm³  Another system of units:        unit of mass =  gm' = 100 gm             unit of length = cm' = 10 cm         and     Substitute these values in the value of the density.  Now density of the material: Thus in the new system the value of density will be 40 units.  
Medical
96 Views   |  

The dimesnions of (\mu_{o} \epsilon_{o} )^{\frac{-1}{2}}\;are

  • Option 1)

    \left [ L^{\frac{1}{2}}T^{-\frac{1}{2}} \right ]

  • Option 2)

    \left [ L^{-1} \right T ]

  • Option 3)

    \left [ LT^{-1} \right ]

  • Option 4)

    \left [ L^{-\frac{1}{2}}T^{\frac{1}{2}} \right ]

 
As learnt in Dimension - The power to which fundamental quantities must be raised in order to express the given physical quantities. -       Option 1) This option is incorrect Option 2) This option is incorrect Option 3) This option is correct Option 4) This option is incorrect
Medical
88 Views   |  

The dimension of \frac{1}{2}\epsilon _{o}E^{2} where \varepsilon _{o} is permittivity of free space and E is electric field, is:

  • Option 1)

    ML2T-2

  • Option 2)

    ML-1T-2

  • Option 3)

    ML2T-1

  • Option 4)

    MLT-1

 
As we learnt in Dimension - The power to which fundamental quantities must be raised in order to express the given physical quantities. -       Option 1) ML2T-2 Incorrect Option 2) ML-1T-2 Correct Option 3) ML2T-1 Incorrect Option 4) MLT-1 Incorrect
Medical
1632 Views   |  

The density of material in CGS system of units is 4g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be 

  • Option 1)

    0.4

  • Option 2)

    40

  • Option 3)

    400

  • Option 4)

    0.04

 

Option 2=40

 

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