A massive black hole of mass m and radius R isspinning with angular velocity ω. The power Pradiated by it as gravitational waves is given byP = Gc^{–5}m^xR^y\omega^z , where c and G are speed of light in free space, and the universal gravitational constant , respectively. Then

Correct Answer is : x = 2, y = 4, z = 6

KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 22 of 120

Marks: +1, -0

A massive black hole of mass m and radius R isspinning with angular velocity ω. The power Pradiated by it as gravitational waves is given by

P = Gc^{–5}m^xR^yω^z

, where c and G are speed of light in free space, and the universal gravitational constant , respectively. Then

Solution:

P = ML^2 T ^{–3} , c = LT^{–1} , ω = T^{–1} , R = L,

m = M

G = M ^{–1} L^3 T^{–2}

[ML^2 T ^{–3} ] = [M^{–1} L^ 3 T ^{–2} ] [LT^{–1} ] ^{–5} M^x L^ y T^{–z}

solve we get x = 2, y = 4, z = 6

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