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In SI units, the dimension of is

  • Option 1)

  • Option 2)

    M^{-1}L^{2}T^{3}A

  • Option 3)

    M^{-1}L^{2}T^{5}A^{2}

  • Option 4)

    M^{-1}L^{2}T^{-3}A

Option 1)Option 2)Option 3)Option 4)

In the formula X=5YZ^{2},X\, \, and\, \, Z have diamension of capacitance and magnetic field, respectively .What are the diamension of Y in SI units?

 

 

 

 

 

 

 

 

 

  • Option 1)

    \left [ M^{-3} L^{-2}T^{8}A^{4}\right ]

  • Option 2)

    \left [ M^{-1} L^{-2}T^{4}A^{2}\right ]

  • Option 3)

    \left [ M^{-2} L^{0}T^{-4}A^{-2}\right ]

  • Option 4)

    \left [ M^{-2} L^{-2}T^{6}A^{3}\right ]

 
Option 1) Option 2) Option 3) Option 4)

If surface tension(S), Momentent of Inertia (I) and Plank's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

  • Option 1)

    S^{\frac{1}{2}}I^{\frac{3}{2}}h^{-1}

  • Option 2)

    S^{\frac{1}{2}}I^{\frac{1}{2}}h^{-1}

  • Option 3)

    S^{\frac{1}{2}}I^{\frac{1}{2}}h^{0}

  • Option 4)

    S^{\frac{3}{2}}I^{\frac{1}{2}}h^{-1}

  Surface tension, surface energy - -     T =surface tension  Option 1) Option 2) Option 3) Option 4)

In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillation is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:

  • Option 1)

    0.7%

  • Option 2)

    0.2%

  • Option 3)

    3.5%

  • Option 4)

    6.8%

      =7 %Option 1)0.7%Option 2)0.2%Option 3)3.5%Option 4)6.8%

The area of a square is 5.29\:\:cm^{2}. The area of 7 such squares taking into account the significant figures is :

  • Option 1)

    37\:\:cm^{2}

  • Option 2)

    37.030\:\:cm^{2}

  • Option 3)

    37.03\:\:cm^{2}

  • Option 4)

    37.0\:\:cm^{2}

 
The significant digit rule says that the number of terms beyond decimal should be equal in final answer after the addition of 7 terms Option 1) Option 2) Option 3) Option 4)

In SI units, the dimensions of \sqrt{\frac{\epsilon _{0}}{\mu _{0}}} is :
 

  • Option 1)

    AT^{-3}ML^{3/2}

  • Option 2)

    AT^{2}M^{-1}L^{-1}

  • Option 3)

    A^{-1}TML^{3}

     

  • Option 4)

    A^{2}T^{3}M^{-1}L^{-2}

We know Option 1)Option 2)Option 3)  Option 4)

In the density measurement of a cube, the mass and edge length are measured as \left ( 10.00\pm 0.10 \right )kg and \left ( 0.10\pm 0.01 \right )m, respectively. The error in the measurement of density is :

  • Option 1)

     0.01\: kg/m^{3}

  • Option 2)

     0.10\: kg/m^{3}

  • Option 3)

    0.31\: kg/m^{3}

  • Option 4)

     0.07\: kg/m^{3}

 
                                                                                   Option 1)   Option 2)   Option 3) Option 4)  
Dimension of Energy = Dimension of Work W = F.l If units of force and length increases 4 times then, W = 4F.4l = 16F.l  Hence unit of Energy will increase 16 times
The initial and final temprature of an oil bath are 25 ± 0.1 0C and 50 ± 0.20C respectively. What
is the percentage error in rise of temprature of the oil bath ?

convert the error to percentage.  max error always gets added, so add errors after converting the error to percentage. 

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A= \frac{p^{3}Q^{2}}{\sqrt{R}S}

@Anmol =   

A physical quantity p depends on otehr two physical quantities Q and R , as follows P = a Q ^2 R^{ 1/2} Where a is constant . In an experiment , the quantity Q is determined by measuring P and R and using The above expression . If the percentage of error in measurment of P and R are 10 % and 12 % respectively , Then the % age of error in determines value of Q is

@Anmol  Given P = 
What is dimensional formula of permeability of free space. Give its explanation ?

@Vijay

Magnetic Field Due to a Straight Wire

B=\frac{\mu_{o}i}{4\pi r}(\sin\phi_{1}+\sin\phi_{2})

you can use any relation that includes permeability of free space to obtain dimensional formula

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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 = Cln(BD) holds true. Then which of the combination is not a meaningful quantity?

@Vijay Hence &   Relevent Concept here is : Dimension - The power to which fundamental quantities must be raised in order to express the given physical quantities. in the  the dimensions of A are not same as dimensions of C meaningless -     Cin(B.D) = are imensionles
1 foot is equal to =0.3048 m and 1 pound is equal to=0.453592 kg
The value of G in CGS system is ​​​​​​​ . Its value in SI units is 6.67 \times 10^{n} .What is the value of n
@Ritesh Dimensional formula =  Simplyfying 

If speed (V), accerleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:

 

  • Option 1)

    V-4 A2F

  • Option 2)

    V-2A2F2

  • Option 3)

    V-2A2F-2

  • Option 4)

     

    V-4A-2F

  To convert a physical quantity from one system to other -   - wherein   &     So  So   Option 1)V-4 A2FOption 2)V-2A2F2Option 3)V-2A2F-2Option 4)  V-4A-2F

The force of interaction between two atoms is given by F = \alpha \beta exp\left [ -\frac{x^{2}}{\alpha kt} \right ]; where x is the distance , k is the Boltzmann constant and T is temperature and \alpha and \beta are two constants. The dimensions of \beta is:

 

  • Option 1)

    M2L2T-2

  • Option 2)

    MLT-2

  • Option 3)

    ML2T-4

  • Option 4)

     

    M2LT-4

  Check the dimensional correctness - - wherein It is based on the principle of homoginity. According to this principle both sides of an equation must be the same .      Option 1)M2L2T-2Option 2)MLT-2Option 3)ML2T-4Option 4)  M2LT-4

 Let l, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of \frac{l}{rcv} in SI units will be : 

  • Option 1)

    [LTA]

  • Option 2)

    [LA-2]

  • Option 3)

    [A-1]

  • Option 4)

    [LT2]

  To convert a physical quantity from one system to other -   - wherein   l - inductance r - resistance c - capacitance v - voltage To find So So Option 1)[LTA]Option 2)[LA-2]Option 3)[A-1]Option 4)[LT2]

The diameter and height of a cylinder are measured by a meter scale to be 12.6\pm 0.1cm and 34.2\pm 0.1cm, respectively. What will be the value of its volume of its volume in appropriate significant figure ?

 

  • Option 1)

    4300\pm 80\: cm^{3}

  • Option 2)

    4264.4\pm 81.0\: cm^{3}

  • Option 3)

    4264\pm 81\: cm^{3}

  • Option 4)

    4260\pm 80\: cm^{3}

  All non zero digits are significant - 42.3     -Three significant figure 238.4     -four significant figure 33.123    -five significant figure -     A zero becomes significant figure if it exists between two non zero digits - 2.09    - Three significant figures 8.206    -four  significant figures 6.002    -four  significant figures - The number of significant figyres in a dismeter and height...

The density of material in SI unit is 128kg m-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is:

 

  • Option 1)

     

    40

  • Option 2)

     

    16

  • Option 3)

     

    640

  • Option 4)

     

    410

     

  Physical quantity, n u =constant -   now 50g equal to 1 unit of mass so 1g equal to unit of mass Similarly 25cm equal to 1 unit of length so 1cm equal to unit of length so    so put in equation no.(1)     so ans is 40 -    Option 1)  40Option 2)  16Option 3)  640Option 4)  410  
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