Home
Class 11
PHYSICS
The dimensions of the area A of a black ...

The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G, its mass M and the speed of light c as `A=G^(alpha)M^(beta)c^(gamma)`. Here -

A

`alpha = -2,beta = -2 and gamma = 4`

B

`alpha = 2,beta = 2 and gamma = -4`

C

`alpha = 3,beta = -3 and gamma = -2`

D

`alpha = -3,beta = -3 and gamma = 2`

Text Solution

Verified by Experts

The correct Answer is:
B
`A = G^(alpha)M^(beta)c^(gamma)`
`L^2=(M^(-1)L^3T^(-2))^(alpha)(M^1)beta(L^1T^(-1))^(gamma)`
`-alpha+beta =0 " "....(i) `
`3alpha+ gamma =2 " "...(ii)`
`-2 alpha - gamma = 0 " "....(iii)`
`alpha =2 , beta = 2 and gamma =-4`
Promotional Banner

Similar Questions

Explore conceptually related problems

The C.G.S. unit of universal gravitational constant is

The dimensions of Stefan-Boltzman constant sigma can be written in terms of Plank's constant h. Boltzmann constant k_(B) and the speed of light c as sigma = h^(alpha) K_(B)^(b) c^(Y) . Here

The dimensions of Stefan-Boltzmann constant sigma can be written in terms of Planck's constant h, Boltzmann constant k_(B) and the speed of light c as sigma = h^(α) k_(B)^(β) c^(gamma) . Here

Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

The dimensional formula of universal gravitational constant 'G' [M^(-1) L^(3) T^(-2)] .

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n( r) = 1+ 2 GM//rc^2 where r is the distance of the point consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object, find the deviation of the ray from the original path as it grazes the object.

The dimensions of length are expressed as G^(x)c^(y)h^(z) , where G, c and h are the universal gravitational constant, speed of light and Planck's constant respectively, then :

The radiation emitted per unit time by unit area of a black body at temperature T is sigmaT^(4) wehre sigma is the Stefan-Boltzmann constant. The constant sigma can also be expressed in terms of Boltmann's constant (k), Planck's constant (h) and speed of light (3) as sigma=Ak^(alpha)h^(beta)c^(gamma) where A, alpha,beta and gamma are dimensionless constants. The set (alpha,beta,gamma) is givne by