Home
Class 11
PHYSICS
In the expression P=Et^2m^-5G^-2 the qua...

In the expression `P=Et^2m^-5G^-2` the quantities E,I,m and G denote energy , angular momentum, mass and gravitational constant respectively. Show that P is a dimensionless quantity.

Text Solution

Verified by Experts

Here , `P=El^2m^-5G^-2`
Here,
I=energy , l=angular momentum
m=mass G = gravitational constant
`=[ML^2T^-2][ML^2T^-1]^2[M]^-5[M^-1L^3T^-2]^-2`
`=M^(1+2+5+2)L^(2+4+6)T^(-2-2+4)`
`P=[M^0L^0T^0]`
Hence, P is a dimensionless quantity.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • UNITS AND MEASUREMENTS

    VGS PUBLICATION-BRILLIANT|Exercise SHORT ANSWER QUESTIONS|10 Videos

  • THERMAL PROPERTIES OF MATTER

    VGS PUBLICATION-BRILLIANT|Exercise LONG ANSWER QUESTIONS|2 Videos

Similar Questions

Explore conceptually related problems

In the expression P=El^(2)m^(-5)G^(-2) the quantities E, l, m and G denote energy, angular momentum, mass and gravitational constant respectively. Show that P is a dimensionless quantity.

If E, M, L and G denote energy, mass, angular momentum and universal Gravitational constant respectively, prove that (EL^(2))/(M^(5)G^(2)) is a dimensionless quantity.

Knowledge Check

  • If E, M, J and G respectively denote energy, mass angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of (EJ^(2))/(M^(5)G^(2))

    A
    Time
    B
    Angle
    C
    Mass
    D
    Length

  • If C the velocity of light,h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

    A
    `h^(-1//2)G^(1//2)C^(0)`
    B
    `h^(1//2)C^(1//2)G^(-1//2)`
    C
    `h^(-1//2)C^(1//2)G^(-1//2)`
    D
    `h^(-1//2)C^(-1//2)G^(-1//2)`

  • If C the velocity of light, h Planck's onstant and G Gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

    A
    `h^(-1//2) G^(1//2) C^(0)`
    B
    `h^(1//2) C^(1//2) G^(-1//2)`
    C
    `h^(-1//2) C^(1//2) G^(-1//2)`
    D
    `h^(-1//2) C^(-1//2) G^(-1//2)`

    • Similar Questions

    Explore conceptually related problems

    If E, M,L and G denote energy, mass, angular momentum and universal Gravitational constant respectively, prove that (EL^(2) )/(M^(5) G^(2) ) is a dimensionless quantity.

    If E, M, L and G denote energy, mass, angular momentum and universal Gravitational constant respectively, prove that (EL^(2))/(M^(5)G^(2)) is a dimensionless quantity .

    If E, M, J and G denote energy, mass, angular momentum and gravitational constant respectively, calculate the dimensions of the quantity (EJ^(2))/(M^(5)G^(2)) .

    Suppose you design your system of dimensions and take velocity (V). Planck constant (h) and gravitational constant (G) as the fundamental quantities . What will be the dimensions of length (L), mass (M) and time (T) in this system ?

    The period T_0 for a planet of mass 'm' above the sum in a circular orbit of radius R depends on m,R and G where G is the gravitational constant. Find expression for time period by dimensional methods.

    Home
    Profile