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If the energy E =G^ph^qc^r where G is the universal gravitational constant ,h is the planks constant and c is the velocity of light ,then the value of p,q,r respectively

If the energy E =G^ph^qc^r where G is the universal gravitational constant ,h is the planks constant and c is the velocity of light ,then the value of p,q,r respectively

Grade:11

1 Answers

Bhavana Bristee Bora
19 Points
6 years ago
E=G^p×h^q×c^r[ML²T-²] = [M-¹L³T-²]^p [ML²T-¹]^q [LT-¹]^r[ML²T-²] = [M^(-p+q) L^(3p+2q+r) T^(-2p-q-r)]Equating the powers of M,L,T, we get-p+q=1q=p+1....(1)Also,3p+2q+r=23p+2(p+1)+r=2....(using equation 1)5p+r=0....(2)Again,-2p-q-r= -22p+q+r=22p+(p+1)+r=2....(using equation 1)3p+r=1....(3)Now,subtracting equation (3) from equation (2), we get5p+r-3p-r=0-12p=-1p=-1/2....(4)Now, from equation (1),we getq=p+1q=-1/2 + 1.... (using equation 4)q=1/2....(5)Also, from equation (2),we get5p+r=05(-1/2)+r=0r=5/2....(6)Hence,from equations (4),(5),(6),we getp=-1/2,q=1/2,r=5/2

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