The dimension of stopping potential V _ 0 in photoelectric effect in units of Planck’s constant ‘ h ’, speed of light ‘ c ’ and Gravitational constant ‘ G ’ and ampere A is:

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The dimension of stopping potential V _ 0 in photoelectric effect in units of Planck&rsquo;s constant &lsquo; h &rsquo;, speed of light &lsquo; c &rsquo; and Gravitational constant &lsquo; G &rsquo; and ampere A is:

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Correct answer: B. h ^ 0 c ^ 5 G ^ - 1 A ^ - 1

V = K ( h ) ^ a ( I ) ^ b ( G ) ^ c ( C ) ^ d (V is voltage) We know [ h ] = M L ^ 2 T ^ - 1 [ I ] = A [ G ] = M ^ - 1 L ^ 3 T ^ - 2 [ C ] = L T ^ - 1 [ V ] = M L ^ 2 T ^ - 3 A ^ - 1 M L ^ 2 T ^ - 3 A ^ - 1 = ( M L ^ 2 T ^ - 1 ) ^ a ( A ) ^ b ( M ^ - 1 L ^ 3 T ^ - 2 ) ^ c ( L T ^ - 1 ) ^ d M L ^ 2 T ^ - 3 A ^ - 1 = M ^ a - c L ^ 2a + 3c + d T ^ - a - 2c - d A ^ b a - c = 1 . . . . . ( 1 ) 2a + 3c + d = 2 . . . . . ( 2 ) - a - 2c - d = - 3 . . . . . ( 3 ) b = - 1 . . . ( 4 ) On solving c = - 1 a = 0 d = 5, b = - 1 V = K ( h ) ^ 0 ( A ) ^ - 1 ( G ) ^ - 1 ( C ) ^ 5

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