KVPY2017PhysicsUnits and Dimensions
A massive black hole of mass m and radius R is spinning with angular velocity . The power P radiated by it as gravitational waves is given by P = Gc ⁻⁵ ~m ^ x R ^ y ^ z , where c and G are speed of light in free space, and the universal gravitational constant, respectively. Then
Options
- Ax=-1, y=2, z=4
- Bx=1, y=1, z=4
- Cx=-1, y=4, z=4
- Dx=2, y=4, z=6
Correct answer
D. x=2, y=4, z=6
Step-by-step solution
P = ML ² ~T ⁻³, c = LT ⁻¹, = 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