SATHEE: Physical World Units and Measurements

Physical World Units and Measurements - Result Question 28

30. P represents radiation pressure, $c$ represents speed of light and $S$ represents radiation energy striking unit area per sec. The non zero integers $x, y, z$ such that $P^{x} S^{y} c^{z}$ is dimensionless are (a) $x = 1, y = 1, z = 1$

(b) $x = - 1, y = 1, z = 1$

(d) $x = 1, y = 1, z = - 1$

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Answer:

Correct Answer: 30. (c)

Solution:

(c) Let the expression, $α = P^{x} S^{y} c^{z}$ ..(i) and given that dimension of $α = [M^{0} L^{0} T^{0}] \dots$ (ii) $=$ dimensionless

Dimension fo radiation pressure $P = \frac{Force}{Area}$

$= \frac{[M L T^{- 2}]}{[L^{2}]} = [M L^{- 1} T^{- 2}]$

Dimension of radiation energy/unit area unit time

$S = \frac{Energy}{Area \times Time} = \frac{[M L^{2} T^{- 2}]}{[L^{2}] [T]} = [M T^{- 3}]$

Dimension of speed of light, $c = [L T^{- 1}]$

By equation (i) we get,

So, the dimension of $α = [M L^{- 1} T^{- 2}]^{x} [M T^{- 3}]^{y}$

$[L T^{- 1}]^{z}$

According to equation (ii),

$\Rightarrow [M^{0} L^{0} T^{0}] = [M L^{- 1} T^{- 2}]^{x} [M T^{- 3}]^{y} [L T^{- 1}]^{z}$

$\Rightarrow [M^{0} L^{0} T^{0}] = [M^{x + y} L^{- x + z} T^{- 2 x - 3 y - z}]$

Applying the principle of homegenity of dimension we get, $x + y = 0$ $- x + z = 0$ $- 2 x - 3 y - z = 0$

After solving above three equation we get, $x = 1; y = - 1; z = 1$

Try out the given alternatives. When $x = 1, y = - 1, z = 1$

$\begin{aligned} P^{x} y_{c^{z}} & = P^{1} S^{- 1} c^{1} = \frac{P c}{S} \\ = \frac{[M L^{- 1} T^{- 2}] [L T^{- 1}]}{[M L^{2} T^{- 2} / L^{2} T]} = [M^{0} L^{0} T^{0}] \end{aligned}$

Physical World Units and Measurements - Result Question 28

30. P represents radiation pressure, $c$ represents speed of light and $S$ represents radiation energy striking unit area per sec. The non zero integers $x, y, z$ such that $P^{x} S^{y} c^{z}$ is dimensionless are (a) $x = 1, y = 1, z = 1$

Answer:

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Physical World Units and Measurements - Result Question 28

30. P represents radiation pressure, c represents speed of light and S represents radiation energy striking unit area per sec. The non zero integers x,y,z such that PxSycz is dimensionless are (a) x=1,y=1,z=1

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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30. P represents radiation pressure, $c$ represents speed of light and $S$ represents radiation energy striking unit area per sec. The non zero integers $x, y, z$ such that $P^{x} S^{y} c^{z}$ is dimensionless are (a) $x = 1, y = 1, z = 1$