Home
Class 11
PHYSICS
In the expression P=El^(2)m^(-5)G^(-2),E...

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

Text Solution

Verified by Experts

Givet, expression is `P=EL^(2)m^(-5)G^(-2)`
where E is energy `[E]=[M^(1)L^(2)T^(-2)]`
m is mass `[m]=[M^(1)]`
L is angular moment `[L][M^(1)L^(2)T^(-1)]`
G is gratvittional constant `[G]=[M^(1)L^(3)T^(-2)]`
Substituting dimensions of each term in the given expression
`[P]=[M^(1)L^(2)T^(-2)]xx[M^(1)L^(2)T^(-1)]xx[M^(1)]^(-5)xx[M^(-1)L^(3)T^(-2)]^(-2)`
`=[M^(1+2-5+2)L^(2+4-6)T^(-2-2+4)]=[M^(0)L^(0)T^(0)]`
Hence P is a dimensionless quantity.
Promotional Banner

Topper's Solved these Questions

  • UNITS AND MEASUREMENT

    KUMAR PRAKASHAN|Exercise SECTION -E (MULTIPLE CHOICE QUESTIONS (MCQS) (MCQS ASKED IN GUJARAT BOARD AND COMPETITIVE EXAMS)|66 Videos

  • UNITS AND MEASUREMENT

    KUMAR PRAKASHAN|Exercise Section -F (Questions from Module )|20 Videos

  • UNITS AND MEASUREMENT

    KUMAR PRAKASHAN|Exercise SECTION -D (NECERT EXEMPLAR SOLUTIONS) (Short Answer Type Questions)|13 Videos

  • THERMODYANMICS

    KUMAR PRAKASHAN|Exercise Question Paper|11 Videos

  • WAVES

    KUMAR PRAKASHAN|Exercise SECTION-F (Questions From Module) (Sample questions for preparation of competitive exams)|23 Videos

Similar Questions

Explore conceptually related problems

(a) In the formula X=3YZ^(2) , X and Z have dimensions of capcitnce and magnetic inlduction, respectively. What are the dimensions of Y in MKSQ system? (b) A qunatity X is given by epsilon_(0) L ((Delta)V)/((Delta)r) , where epsilon_(0) is the permittivity of free space, L is a lenght, DeltaV is a potential difference and Deltat is a time interval. Find the dimensions of X . (c) If E,M,J and G denote energy , mass , angular momentum and gravitational constant, respectively. find dimensons of (E J^(2))/(M^(5) G^(2)) (d) If e,h,c and epsilon_(0) are electronic charge, Planck 's constant speed of light and permittivity of free space. Find the dimensions of (e^(2))/(2epsilon_(0)hc) .

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

The 5^(th), 8^(th) and 11^(th) terms of a G.P are p,q and s , respectively . Show that q^2 =ps .

If C_(p) and C_(v) denoted the specific heats of unit mass of nitrogen at constant pressure and volume respectively, then

If velocity of light c, Planck's constant h and gravitational constant G are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.

The frequency of oscillation of a mass m suspended from a spring having force constant k is given by f = Cm^(x)k^(g) , where C is a dimensionless quantity. The value of x and y

In K=(p^(2))/(2m) find the relative error. (Take mass m, constant)

It is known that the time of revolution T of a satellite around the earth depends on the universal gravitational constant G, the mass of the earth M, and the radius of the circular orbit R. Obtain an expression for T using dimensional analysis.

If the energy, E = G^p h^q c^r, where G is the universal gravitational constant, h is the Planck's constant and c is the velocity of light, then the values of p are q and r are, respectively

The angular momentum of a wheel changes from 2L to 5L in 3 seconds. What will be the magnitude of torque acting on it?