KVPY SX SB Exam 2015 Question Paper

Question : 36 of 120

Marks: +1, -0

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^αM^βc^γ

. Here -

$α = -2, β =-2, \and γ = 4$
$α = 2, β = 2, \and γ = -4$
$α = 3, β = 3, \andγ = -2$
$α = -3, β = -3, \andγ = 2$

Validate

Solution:

A = Gα Mβ Cγ

[M^0 L^ 2 T^ 0 ] = [M^{-1} L^ 3 T ^{-2} ]^α [M]^β [LT^{-1} ] ^γ

-α + β = 0 ⇒α = β

3α + γ = 2

-2α - γ = 0

on solving

α = 2, β = 2, γ = -4

Go to Question:

Prev Question

Next Question