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Universal gravitational constant

In form of G (universal gravitational constant), h (Planck con

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Solving time: 3 mins

In form of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light), the time period will be proportional to
(a) $\frac{G h}{c ^{5}}$
(b) $\frac{h c ^{5}}{G}$
(c) $\frac{c ^{3}}{G h}$
(d) $\frac{G h}{c ^{3}}$

Views: 6,114 students

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

Found 3 tutors discussing this question

Chloe Discussed

In form of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light), the time period will be proportional to
(a)

\frac{G h}{c ^{5}}

(b)

\frac{h c ^{5}}{G}

(c)

\frac{c ^{3}}{G h}

(d)

\frac{G h}{c ^{3}}

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Exp. (a)
Key Idea According to dimensional analysis, if a physical quantity (let y) depends on another physical quantities (let

A, B, C

), then the dimension formula is given by

y = A^{a} B^{b} C^{c}

(where,

a, b, c

are the power of physical quantity and

k =

constant)
For the given question, the time (t) depends on the G (gravitational constant),

h

(Planck's constant) and

c

(velocity of light), then according to dimensional analysis

t = k (G)^{a} (h)^{b} (c)^{c}

For calculating the values of

a, b

and

c

, compare the dimensional formula for both side.
LHS

t = t im e = [M^{0} L^{0} T^{1}]

RHS

G = \frac{F \cdot r ^{2}}{m _{1} m _{2}} = \frac{kg ms ^{- 2} \times m ^{2}}{( kg ) ^{2}} = [M^{- 1} L^{3} T^{- 2}]^{a}

h = [M^{1} L^{2} T^{- 1}]^{b}

c = \frac{d}{t} = [M^{0} L^{1} T^{- 1} F

Compare both side for powers of

M, L

and

T

M \Rightarrow 0 = - a + b

L \Rightarrow 0 = 3 a + 2 b + c

T \Rightarrow 1 = - 2 a - b - c

Solving Eqs. (i), (ii), (iii), we get

a = \frac{1}{2}, b = \frac{1}{2}

and

c = \frac{- 5}{2}

So, put these values in Eq. (i), we get

t = k G^{1/2} h^{1/2} c^{- 5/2}

t = k \frac{G h}{c ^{5}}

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Question Text	In form of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light), the time period will be proportional to (a) $\frac{G h}{c ^{5}}$ (b) $\frac{h c ^{5}}{G}$ (c) $\frac{c ^{3}}{G h}$ (d) $\frac{G h}{c ^{3}}$
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	33

In form of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light), the time period will be proportional to
(a) $\frac{G h}{c ^{5}}$
(b) $\frac{h c ^{5}}{G}$
(c) $\frac{c ^{3}}{G h}$
(d) $\frac{G h}{c ^{3}}$

Text solutionVerified

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Text solutionVerified

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In form of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light), the time period will be proportional to
(a) $\frac{G h}{c ^{5}}$
(b) $\frac{h c ^{5}}{G}$
(c) $\frac{c ^{3}}{G h}$
(d) $\frac{G h}{c ^{3}}$