If p represents radiation pressure, C represents the speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a,b and c are such that paqbCc is dimensionless, then

Question

If p represents radiation pressure, C represents the speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a,b and c are such that paqbCc is dimensionless, then (A) a=1,b=1,c=-1 (B) a=1,b=-1,c=1 (C) a=-1,b=1,c=1 (D) a=1,b=1,c=1

Tardigrade Admin · Accepted Answer

Here, [M0 L0 T0]=[M L- 1 T- 2]a[M T- 3]b[L T- 1]c Or [M0 L0 T0]=[. Ma + bL- a + cT- 2 a - 3 b - c ] Comparing powers of M,L and T, we get a+b=0,-a+c=0,-2a-3b=0 Solving a=1,b=-1,c=1

Q. If $p$ represents radiation pressure, $C$ represents the speed of light and $q$ represents radiation energy striking a unit area per second, then non-zero integers $a, b$ and $c$ are such that $p^{a} q^{b} C^{c}$ is dimensionless, then

$a = 1, b = 1, c = - 1$

$a = 1, b = - 1, c = 1$

$a = - 1, b = 1, c = 1$

$a = 1, b = 1, c = 1$

Here, $[M^{0} L^{0} T^{0}] = [M L^{- 1} T^{- 2}]^{a} [M T^{- 3}]^{b} [L T^{- 1}]^{c}$
Or $[M^{0} L^{0} T^{0}] = [M^{a + b} L^{- a + c} T^{- 2 a - 3 b - c}$ ]
Comparing powers of $M, L$ and $T,$ we get
$a + b = 0, - a + c = 0, - 2 a - 3 b = 0$
Solving $a = 1, b = - 1, c = 1$

Q. If p represents radiation pressure, C represents the speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a,b and c are such that paqbCc is dimensionless, then

a=1,b=1,c=−1

a=1,b=−1,c=1

a=−1,b=1,c=1

a=1,b=1,c=1